nips nips2011 nips2011-90 knowledge-graph by maker-knowledge-mining

90 nips-2011-Evaluating the inverse decision-making approach to preference learning

Source: pdf

Author: Alan Jern, Christopher G. Lucas, Charles Kemp

Abstract: Psychologists have recently begun to develop computational accounts of how people infer others’ preferences from their behavior. The inverse decision-making approach proposes that people infer preferences by inverting a generative model of decision-making. Existing data sets, however, do not provide sufﬁcient resolution to thoroughly evaluate this approach. We introduce a new preference learning task that provides a benchmark for evaluating computational accounts and use it to compare the inverse decision-making approach to a feature-based approach, which relies on a discriminative combination of decision features. Our data support the inverse decision-making approach to preference learning. A basic principle of decision-making is that knowing people’s preferences allows us to predict how they will behave: if you know your friend likes comedies and hates horror ﬁlms, you can probably guess which of these options she will choose when she goes to the theater. Often, however, we do not know what other people like and we can only infer their preferences from their behavior. If you know that a different friend saw a comedy today, does that mean that he likes comedies in general? The conclusion you draw will likely depend on what else was playing and what movie choices he has made in the past. A goal for social cognition research is to develop a computational account of people’s ability to infer others’ preferences. One computational approach is based on inverse decision-making. This approach begins with a model of how someone’s preferences lead to a decision. Then, this model is inverted to determine the most likely preferences that motivated an observed decision. An alternative approach might simply learn a functional mapping between features of an observed decision and the preferences that motivated it. For instance, in your friend’s decision to see a comedy, perhaps the more movie options he turned down, the more likely it is that he has a true preference for comedies. The difference between the inverse decision-making approach and the feature-based approach maps onto the standard dichotomy between generative and discriminative models. Economists have developed an instance of the inverse decision-making approach known as the multinomial logit model [1] that has been widely used to infer consumer’s preferences from their choices. This model has recently been explored as a psychological model [2, 3, 4], but there are few behavioral data sets for evaluating it as a model of how people learn others’ preferences. Additionally, the data sets that do exist tend to be drawn from the developmental literature, which focuses on simple tasks that collect only one or two judgments from children [5, 6, 7]. The limitations of these data sets make it difﬁcult to evaluate the multinomial logit model with respect to alternative accounts of preference learning like the feature-based approach. In this paper, we use data from a new experimental task that elicits a detailed set of preference judgments from a single participant in order to evaluate the predictions of several preference learning models from both the inverse decision-making and feature-based classes. Our task requires each participant to sort a large number of observed decisions on the basis of how strongly they indicate 1 (a) (b) (c) d c c (d) b b a a x d x d c b a x 1. Number of chosen effects (−/+) 2. Number of forgone effects (+/+) 3. Number of forgone options (+/+) 4. Number of forgone options containing x (−/−) 5. Max/min number of effects in a forgone option (+/−) 6. Is x in every option? (−/−) 7. Chose only option with x? (+/+) 8. Is x the only difference between options? (+/+) 9. Do all options have same number of effects? (+/+) 10. Chose option with max/min number of effects? (−/−) Figure 1: (a)–(c) Examples of the decisions used in the experiments. Each column represents one option and the boxes represent different effects. The chosen option is indicated by the black rectangle. (d) Features used by the weighted feature and ranked feature models. Features 5 and 10 involved maxima in Experiment 1, which focused on all positive effects, and minima in Experiment 2, which focused on all negative effects. The signs in parentheses indicate the direction of the feature that suggests a stronger preference in Experiment 1 / Experiment 2. a preference for a chosen item. Because the number of decisions is large and these decisions vary on multiple dimensions, predicting how people will order them offers a challenging benchmark on which to compare computational models of preference learning. Data sets from these sorts of detailed tasks have proved fruitful in other domains. For example, data reported by Shepard, Hovland, and Jenkins [8]; Osherson, Smith, Wilkie, L´ pez, and Shaﬁr [9]; and Wasserman, Elek, Chatlosh, o and Baker [10] have motivated much subsequent research on category learning, inductive reasoning, and causal reasoning, respectively. We ﬁrst describe our preference learning task in detail. We then present several inverse decisionmaking and feature-based models of preference learning and compare these models’ predictions to people’s judgments in two experiments. The data are well predicted by models that follow the inverse decision-making approach, suggesting that this computational approach may help explain how people learn others’ preferences. 1 Multi-attribute decisions and revealed preferences We designed a task that can be used to elicit a large number of preference judgments from a single participant. The task involves a set of observed multi-attribute decisions, some examples of which are represented visually in Figure 1. Each decision is among a set of options and each option produces a set of effects. Figure 1 shows several decisions involving a total of ﬁve effects distributed among up to ﬁve options. The differently colored boxes represent different effects and the chosen option is marked by a black rectangle. For example, 1a shows a choice between an option with four effects and an option with a single effect; here, the decision maker chose the second option. In our task, people are asked to rank a large number of these decisions by how strongly they suggest that the decision maker had a preference for a particular effect (e.g., effect x in Figure 1). By imposing some minimal constraints, the space of unique multi-attribute decisions is ﬁnite and we can obtain rankings for every decision in the space. For example, Figure 2c shows a complete list of 47 unique decisions involving up to ﬁve effects, subject to several constraints described later. Three of these decisions are shown in Figure 1. If all the effects are positive—pieces of candy, for example—the ﬁrst decision (1a) suggests a strong preference for candy x, because the decision maker turned down four pieces in favor of one. The second decision (1b), however, offers much weaker evidence because nearly everyone would choose four pieces of candy over one, even without a speciﬁc preference for x. The third decision (1c) provides evidence that is strong but perhaps not quite as strong as the ﬁrst decision. When all effects are negative—like electric shocks at different body locations—decision makers may still ﬁnd some effects more tolerable than others, but different inferences are sometimes supported. For example, for negative effects, 1a provides weak evidence that x is relatively tolerable because nearly everyone would choose one shock over four. 2 A computational account of preference learning We now describe a simple computational model for learning a person’s preferences after observing that person make a decision like the ones in Figure 1. We assume that there are n available options 2 {o1 , . . . , on }, each of which produces one or more effects from the set {f1 , f2 , ..., fm }. For simplicity, we assume that effects are binary. Let ui denote the utility the decision maker assigns to effect fi . We begin by specifying a model of decision-making that makes the standard assumptions that decision makers tend to choose things with greater utility and that utilities are additive. That is, if fj is a binary vector indicating the effects produced by option oj and u is a vector of utilities assigned to each of the m effects, then the total utility associated with option oj can be expressed as Uj = fj T u. We complete the speciﬁcation of the model by applying the Luce choice rule [11], a common psychological model of choice behavior, as the function that chooses among the options: p(c = oj |u, f ) = exp(Uj ) = exp(Uk ) n k=1 exp(fj T u) n T k=1 exp(fk u) (1) where c denotes the choice made. This model can predict the choice someone will make among a speciﬁed set of options, given the utilities that person assigns to the effects in each option. To obtain estimates of someone’s utilities, we invert this model by applying Bayes’ rule: p(u|c, F) = p(c|u, F)p(u) p(c|F) (2) where F = {f1 , . . . , fn } speciﬁes the available options and their corresponding effects. This is the multinomial logit model [1], a standard econometric model. In order to apply Equation 2 we must specify a prior p(u) on the utilities. We adopt a standard approach that places independent Gaussian priors on the utilities: ui ∼ N (µ, σ 2 ). For decisions where effects are positive—like candies—we set µ = 2σ, which corresponds to a prior distribution that places approximately 2% of the probability mass below zero. Similarly, for negative effects—like electric shocks—we set µ = −2σ. 2.1 Ordering a set of observed decisions Equation 2 speciﬁes a posterior probability distribution over utilities for a single observed decision but does not provide a way to compare the inferences drawn from multiple decisions for the purposes of ordering them. Suppose we are interested in a decision maker’s preference for effect x and we wish to order a set of decisions by how strongly they support this preference. Two criteria for ordering the decisions are as follows: Absolute utility Relative utility p(c|ux , F)p(ux ) p(c|F) p(c|∀j ux ≥ uj , F)p(∀j ux ≥ uj ) p(∀j ux ≥ uj |c, F) = p(c|F) E(ux |c, F) = Eux The absolute utility model orders decisions by the mean posterior utility for effect x. This criterion is perhaps the most natural way to assess how much a decision indicates a preference for x, but it requires an inference about the utility of x in isolation, and research suggests that people often think about the utility of an effect only in relation to other salient possibilities [12]. The relative utility model applies this idea to preference learning by ordering decisions based on how strongly they suggest that x has a greater utility than all other effects. The decisions in Figures 1b and 1c are cases where the two models lead to different predictions. If the effects are all negative (e.g., electric shocks), the absolute utility model predicts that 1b provides stronger evidence for a tolerance for x because the decision maker chose to receive four shocks instead of just one. The relative utility model predicts that 1c provides stronger evidence because 1b offers no way to determine the relative tolerance of the four chosen effects with respect to one another. Like all generative models, the absolute and relative models incorporate three qualitatively different components: the likelihood term p(c|u, F), the prior p(u), and the reciprocal of the marginal likelihood 1/p(c|F). We assume that the total number of effects is ﬁxed in advance and, as a result, the prior term will be the same for all decisions that we consider. The two other components, however, will vary across decisions. The inverse decision-making approach predicts that both components should inﬂuence preference judgments, and we will test this prediction by comparing our 3 two inverse decision-making models to two alternatives that rely only one of these components as an ordering criterion: p(c|∀j ux ≥ uj , F) 1/p(c|F) Representativeness Surprise The representativeness model captures how likely the observed decision would be if the utility for x were high, and previous research has shown that people sometimes rely on a representativeness computation of this kind [13]. The surprise model captures how unexpected the observed decision is overall; surprising decisions may be best explained in terms of a strong preference for x, but unsurprising decisions provide little information about x in particular. 2.2 Feature-based models We also consider a class of feature-based models that use surface features to order decisions. The ten features that we consider are shown in Figure 1d, where x is the effect of interest. As an example, the ﬁrst feature speciﬁes the number of effects chosen; because x is always among the chosen effects, decisions where few or no other effects belong to the chosen option suggest the strongest preference for x (when all effects are positive). This and the second feature were previously identiﬁed by Newtson [14]; we included the eight additional features shown in Figure 1d in an attempt to include all possible features that seemed both simple and relevant. We consider two methods for combining this set of features to order a set of decisions by how strongly they suggest a preference for x. The ﬁrst model is a standard linear regression model, which we refer to as the weighted feature model. The model learns a weight for each feature, and the rank of a given decision is determined by a weighted sum of its features. The second model is a ranked feature model that sorts the observed decisions with respect to a strict ranking of the features. The top-ranked feature corresponds to the primary sort key, the second-ranked feature to the secondary sort key, and so on. For example, suppose that the top-ranked feature is the number of chosen effects and the second-ranked feature is the number of forgone options. Sorting the three decisions in Figure 1 according to this criterion produces the following ordering: 1a,1c,1b. This notion of sorting items on the basis of ranked features has been applied before to decision-making [15, 16] and other domains of psychology [17], but we are not aware of any previous applications to preference learning. Although our inverse decision-making and feature-based models represent two very different approaches, both may turn out to be valuable. An inverse decision-making approach may be the appropriate account of preference learning at Marr’s [18] computational level, and a feature-based approach may capture the psychological processes by which the computational-level account is implemented. Our goal, therefore, is not necessarily to accept one of these approaches and dismiss the other. Instead, we entertain three distinct possibilities. First, both approaches may account well for the data, which would support the idea that they are valid accounts operating at different levels of analysis. Second, the inverse decision-making approach may offer a better account, suggesting that process-level accounts other than the feature-based approach should be explored. Finally, the feature-based approach may offer a better account, suggesting that inverse decision-making does not constitute an appropriate computational-level account of preference learning. 3 Experiment 1: Positive effects Our ﬁrst experiment focuses on decisions involving only positive effects. The full set of 47 decisions we used is shown in Figure 2c. This set includes every possible unique decision with up to ﬁve different effects, subject to the following constraints: (1) one of the effects (effect x) must always appear in the chosen option, (2) there are no repeated options, (3) each effect may appear in an option at most once, (4) only effects in the chosen option may be repeated in other options, and (5) when effects appear in multiple options, the number of effects is held constant across options. The ﬁrst constraint is necessary for the sorting task, the second two constraints create a ﬁnite space of decisions, and the ﬁnal two constraints limit attention to what we deemed the most interesting cases. Method 43 Carnegie Mellon undergraduates participated for course credit. Each participant was given a set of cards, with one decision printed on each card. The decisions were represented visually 4 (a) (c) Decisions 42 40 45 Mean human rankings 38 30 23 20 22 17 13 12 11 10 9 8 7 6 19 18 31 34 28 21 26 36 35 33 37 27 29 32 25 24 16 15 14 5 4 3 2 1 Absolute utility model rankings (b) Mean human rankings (Experiment 1) 47 43 44 46 45 38 37 36 34 35 30 32 33 31 29 28 24 26 27 25 21 19 22 20 18 16 17 12 13 7 6 11 5 9 4 10 8 1 2 3 42 40 41 39 47 46 44 41 43 39 23 15 14 Mean human rankings (Experiment 2) 1. dcbax 2. cbax 3. bax 4. ax 5. x 6. dcax | bcax 7. dx | cx | bx | ax 8. cax | bax 9. bdx | bcx | bax 10. dcx | bax 11. bx | ax 12. bdx | cax | bax 13. cx | bx | ax 14. d | cbax 15. c | bax 16. b | ax 17. d | c | bax 18. dc | bax 19. c | b | ax 20. dc | bx | ax 21. bdc | bax 22. ad | cx | bx | ax 23. d | c | b | ax 24. bad | bcx | bax 25. ac | bx | ax 26. cb | ax 27. cbad | cbax 28. dc | b | ax 29. ad | ac | bx | ax 30. ab | ax 31. bad | bax 32. dc | ab | ax 33. dcb | ax 34. a | x 35. bad | bac | bax 36. ac | ab | ax 37. ad | ac | ab | ax 38. b | a | x 39. ba | x 40. c | b | a | x 41. cb | a | x 42. d | c | b | a | x 43. cba | x 44. dc | ba | x 45. dc | b | a | x 46. dcb | a | x 47. dcba | x Figure 2: (a) Comparison between the absolute utility model rankings and the mean human rankings for Experiment 1. Each point represents one decision, numbered with respect to the list in panel c. (b) Comparison between the mean human rankings in Experiments 1 and 2. In both scatter plots, the solid diagonal lines indicate a perfect correspondence between the two sets of rankings. (c) The complete set of decisions, ordered by the mean human rankings from Experiment 1. Options are separated by vertical bars and the chosen option is always at the far right. Participants were always asked about a preference for effect x. as in Figure 1 but without the letter labels. Participants were told that the effects were different types of candy and each option was a bag containing one or more pieces of candy. They were asked to sort the cards by how strongly each decision suggested that the decision maker liked a particular target candy, labeled x in Figure 2c. They sorted the cards freely on a table but reported their ﬁnal rankings by writing them on a sheet of paper, from weakest to strongest evidence. They were instructed to order the cards as completely as possible, but were told that they could assign the same ranking to a set of cards if they believed those cards provided equal evidence. 3.1 Results Two participants were excluded as outliers based on the criterion that their rankings for at least ﬁve decisions were at least three standard deviations from the mean rankings. We performed a hierarchical clustering analysis of the remaining 41 participants’ rankings using rank correlation as a similarity metric. Participants’ rankings were highly correlated: cutting the resulting dendrogram at 0.2 resulted in one cluster that included 33 participants and the second largest cluster included 5 Surprise MAE = 17.8 MAE = 7.0 MAE = 4.3 MAE = 17.3 MAE = 9.5 Human rankings Experiment 2 Negative effects Representativeness MAE = 2.3 MAE = 6.7 Experiment 1 Positive effects Relative utility MAE = 2.3 Human rankings Absolute utility Model rankings Model rankings Model rankings Model rankings Figure 3: Comparison between human rankings in both experiments and predicted rankings from four models. The solid diagonal lines indicate a perfect correspondence between human and model rankings. only 3 participants. Thus, we grouped all participants together and analyzed their mean rankings. The 0.2 threshold was chosen because it produced the most informative clustering in Experiment 2. Inverse decision-making models We implemented the inverse decision-making models using importance sampling with 5 million samples drawn from the prior distribution p(u). Because all the effects were positive, we used a prior on utilities that placed nearly all probability mass above zero (µ = 4, σ = 2). The mean human rankings are compared with the absolute utility model rankings in Figure 2a, and the mean human rankings are listed in order in 2c. Fractional rankings were used for both the human data and the model predictions. The human rankings in the ﬁgure are the means of participants’ fractional rankings. The ﬁrst row of Figure 3 contains similar plots that allow comparison of the four models we considered. In these plots, the solid diagonal lines indicate a perfect correspondence between model and human rankings. Thus, the largest deviations from this line represent the largest deviations in the data from the model’s predictions. Figure 3 shows that the absolute and relative utility models make virtually identical predictions and both models provide a strong account of the human rankings as measured by mean absolute error (MAE = 2.3 in both cases). Moreover, both models correctly predict the highest ranked decision and the set of lowest ranked decisions. The only clear discrepancy between the model predictions and the data is the cluster of points at the lower left, labeled as Decisions 6–13 in Figure 2a. These are all cases in which effect x appears in all options and therefore these decisions provide no information about a decision maker’s preference for x. Consequently, the models assign the same ranking to this group as to the group of decisions in which there is only a single option (Decisions 1–5). Although people appeared to treat these groups somewhat differently, the models still correctly predict that the entire group of decisions 1–13 is ranked lower than all other decisions. The surprise and representativeness models do not perform nearly as well (MAE = 7.0 and 17.8, respectively). Although the surprise model captures some of the general trends in the human rankings, it makes several major errors. For example, consider Decision 7: dx|cx|bx|ax. This decision provides no information about a preference for x because it appears in every option. The decision is surprising, however, because a decision maker choosing at random from these options would make the observed choice only 1/4 of the time. The representativeness model performs even worse, primarily because it does not take into account alternative explanations for why an option was chosen, such as the fact that no other options were available (e.g., Decision 1 in Figure 2c). The failure of these models to adequately account for the data suggests that both the likelihood p(c|u, F) and marginal likelihood p(c|F) are important components of the absolute and relative utility models. Feature-based models We compared the performance of the absolute and relative utility models to our two feature-based models: the weighted feature and ranked feature models. For each participant, 6 (b) Ranked feature 10 10 5 Figure 4: Results of the feature-based model analysis from Experiment 1 for (a) the weighted feature models and (b) the ranked feature models. The histograms show the minimum number of features needed to match the accuracy (measured by MAE) of the absolute utility model for each participant. 15 5 1 2 3 4 5 6 >6 15 1 2 3 4 5 6 7 8 9 10 >10 Number of participants (a) Weighted feature Number of features needed we considered every subset of features1 in Figure 1d in order to determine the minimum number of features needed by the two models to achieve the same level of accuracy as the absolute utility model, as measured by mean absolute error. The results of these analyses are shown in Figure 4. For the majority of participants, at least four features were needed by both models to match the accuracy of the absolute utility model. For the weighted feature model, 14 participants could not be ﬁt as well as the absolute utility model even when all ten features were considered. These results indicate that a feature-based account of people’s inferences in our task must be supplied with a relatively large number of features. By contrast, the inverse decision-making approach provides a relatively parsimonious account of the data. 4 Experiment 2: Negative effects Experiment 2 focused on a setting in which all effects are negative, motivated by the fact that the inverse decision-making models predict several major differences in orderings when effects are negative rather than positive. For instance, the absolute utility model’s relative rankings of the decisions in Figures 1a and 1b are reversed when all effects are negative rather than positive. Method 42 Carnegie Mellon undergraduates participated for course credit. The experimental design was identical to Experiment 1 except that participants were told that the effects were electric shocks at different body locations. They were asked to sort the cards on the basis of how strongly each decision suggested that the decision maker ﬁnds shocks at the target location relatively tolerable. The model predictions were derived in the same way as for Experiment 1, but with a prior distribution on utilities that placed nearly all probability mass below zero (µ = −4, σ = 2) to reﬂect the fact that effects were all negative. 4.1 Results Three participants were excluded as outliers by the same criterion applied in Experiment 1. The resulting mean rankings are compared with the corresponding rankings from Experiment 1 in Figure 2b. The ﬁgure shows that responses based on positive and negative effects were substantially different in a number of cases. Figure 3 shows how the mean rankings compare to the predictions of the four models we considered. Although the relative utility model is fairly accurate, no model achieves the same level of accuracy as the absolute and relative utility models in Experiment 1. In addition, the relative utility model provides a poor account of the responses of many individual participants. To better understand responses at the individual level, we repeated the hierarchical clustering analysis described in Experiment 1, which revealed that 29 participants could be grouped into one of four clusters, with the remaining participants each in their own clusters. We analyzed these four clusters independently, excluding the 10 participants that could not be naturally grouped. We compared the mean rankings of each cluster to the absolute and relative utility models, as well as all one- and two-feature weighted feature and ranked feature models. Figure 5 shows that the mean rankings of participants in Cluster 1 (N = 8) were best ﬁt by the absolute utility model, the mean rankings of participants in Cluster 2 (N = 12) were best ﬁt by the relative utility model, and the mean rankings of participants in Clusters 3 (N = 3) and 4 (N = 6) were better ﬁt by feature-based models than by either the absolute or relative utility models. 1 A maximum of six features was considered for the ranked feature model because considering more features was computationally intractable. 7 Cluster 4 N =6 MAE = 4.9 MAE = 14.0 MAE = 7.9 MAE = 5.3 MAE = 2.6 MAE = 13.0 MAE = 6.2 Human rankings Relative utility Cluster 3 N =3 MAE = 2.6 Absolute utility Cluster 2 N = 12 Human rankings Cluster 1 N =8 Factors: 1,3 Factors: 1,8 MAE = 2.3 MAE = 5.2 Model rankings Best−fitting weighted feature Factors: 6,7 MAE = 4.0 Model rankings Model rankings Model rankings Human rankings Factors: 3,8 MAE = 4.8 Figure 5: Comparison between human rankings for four clusters of participants identiﬁed in Experiment 2 and predicted rankings from three models. Each point in the plots corresponds to one decision and the solid diagonal lines indicate a perfect correspondence between human and model rankings. The third row shows the predictions of the best-ﬁtting two-factor weighted feature model for each cluster. The two factors listed refer to Figure 1d. To examine how well the models accounted for individuals’ rankings within each cluster, we compared the predictions of the inverse decision-making models to the best-ﬁtting two-factor featurebased model for each participant. In Cluster 1, 7 out of 8 participants were best ﬁt by the absolute utility model; in Cluster 2, 8 out of 12 participants were best ﬁt by the relative utility model; in Clusters 3 and 4, all participants were better ﬁt by feature-based models. No single feature-based model provided the best ﬁt for more than two participants, suggesting that participants not ﬁt well by the inverse decision-making models were not using a single alternative strategy. Applying the feature-based model analysis from Experiment 1 to the current results revealed that the weighted feature model required an average of 6.0 features to match the performance of the absolute utility model for participants in Cluster 1, and an average of 3.9 features to match the performance of the relative utility model for participants in Cluster 2. Thus, although a single model did not ﬁt all participants well in the current experiment, many participants were ﬁt well by one of the two inverse decision-making models, suggesting that this general approach is useful for explaining how people reason about negative effects as well as positive effects. 5 Conclusion In two experiments, we found that an inverse decision-making approach offered a good computational account of how people make judgments about others’ preferences. Although this approach is conceptually simple, our analyses indicated that it captures the inﬂuence of a fairly large number of relevant decision features. Indeed, the feature-based models that we considered as potential process models of preference learning could only match the performance of the inverse decision-making approach when supplied with a relatively large number of features. We feel that this result rules out the feature-based approach as psychologically implausible, meaning that alternative process-level accounts will need to be explored. One possibility is sampling, which has been proposed as a psychological mechanism for approximating probabilistic inferences [19, 20]. However, even if process models that use large numbers of features are considered plausible, the inverse decision-making approach provides a valuable computational-level account that helps to explain which decision features are informative. Acknowledgments This work was supported in part by the Pittsburgh Life Sciences Greenhouse Opportunity Fund and by NSF grant CDI-0835797. 8 References [1] D. McFadden. Conditional logit analysis of qualitative choice behavior. In P. Zarembka, editor, Frontiers in Econometrics. Amademic Press, New York, 1973. [2] C. G. Lucas, T. L. Grifﬁths, F. Xu, and C. Fawcett. A rational model of preference learning and choice prediction by children. In Proceedings of Neural Information Processing Systems 21, 2009. [3] L. Bergen, O. R. Evans, and J. B. Tenenbaum. Learning structured preferences. In Proceedings of the 32nd Annual Conference of the Cognitive Science Society, 2010. [4] A. Jern and C. Kemp. Decision factors that support preference learning. In Proceedings of the 33rd Annual Conference of the Cognitive Science Society, 2011. [5] T. Kushnir, F. Xu, and H. M. Wellman. Young children use statistical sampling to infer the preferences of other people. Psychological Science, 21(8):1134–1140, 2010. [6] L. Ma and F. Xu. Young children’s use of statistical sampling evidence to infer the subjectivity of preferences. Cognition, in press. [7] M. J. Doherty. Theory of Mind: How Children Understand Others’ Thoughts and Feelings. Psychology Press, New York, 2009. [8] R. N. Shepard, C. I. Hovland, and H. M. Jenkins. Learning and memorization of classiﬁcations. Psychological Monographs, 75, Whole No. 517, 1961. [9] D. N. Osherson, E. E. Smith, O. Wilkie, A. L´ pez, and E. Shaﬁr. Category-based induction. Psychological o Review, 97(2):185–200, 1990. [10] E. A. Wasserman, S. M. Elek, D. L. Chatlosh, and A. G. Baker. Rating causal relations: Role of probability in judgments of response-outcome contingency. Journal of Experimental Psychology: Learning, Memory, and Cognition, 19(1):174–188, 1993. [11] R. D. Luce. Individual choice behavior. John Wiley, 1959. [12] D. Ariely, G. Loewenstein, and D. Prelec. Tom Sawyer and the construction of value. Journal of Economic Behavior & Organization, 60:1–10, 2006. [13] D. Kahneman and A. Tversky. Subjective probability: A judgment of representativeness. Cognitive Psychology, 3(3):430–454, 1972. [14] D. Newtson. Dispositional inference from effects of actions: Effects chosen and effects forgone. Journal of Experimental Social Psychology, 10:489–496, 1974. [15] P. C. Fishburn. Lexicographic orders, utilities and decision rules: A survey. Management Science, 20(11):1442–1471, 1974. [16] G. Gigerenzer and P. M. Todd. Fast and frugal heuristics: The adaptive toolbox. Oxford University Press, New York, 1999. [17] A. Prince and P. Smolensky. Optimality Theory: Constraint Interaction in Generative Grammar. WileyBlackwell, 2004. [18] D. Marr. Vision. W. H. Freeman, San Francisco, 1982. [19] A. N. Sanborn, T. L. Grifﬁths, and D. J. Navarro. Rational approximations to rational models: Alternative algorithms for category learning. Psychological Review, 117:1144–1167, 2010. [20] L. Shi and T. L. Grifﬁths. Neural implementation of Bayesian inference by importance sampling. In Proceedings of Neural Information Processing Systems 22, 2009. 9

Reference: text

Summary: the most important sentenses genereted by tfidf model

sentIndex sentText sentNum sentScore

1 Evaluating the inverse decision-making approach to preference learning Alan Jern Department of Psychology Carnegie Mellon University ajern@cmu. [sent-1, score-0.371]

2 The inverse decision-making approach proposes that people infer preferences by inverting a generative model of decision-making. [sent-7, score-0.33]

3 We introduce a new preference learning task that provides a benchmark for evaluating computational accounts and use it to compare the inverse decision-making approach to a feature-based approach, which relies on a discriminative combination of decision features. [sent-9, score-0.554]

4 Our data support the inverse decision-making approach to preference learning. [sent-10, score-0.371]

5 A basic principle of decision-making is that knowing people’s preferences allows us to predict how they will behave: if you know your friend likes comedies and hates horror ﬁlms, you can probably guess which of these options she will choose when she goes to the theater. [sent-11, score-0.331]

6 For instance, in your friend’s decision to see a comedy, perhaps the more movie options he turned down, the more likely it is that he has a true preference for comedies. [sent-20, score-0.559]

7 The limitations of these data sets make it difﬁcult to evaluate the multinomial logit model with respect to alternative accounts of preference learning like the feature-based approach. [sent-25, score-0.369]

8 In this paper, we use data from a new experimental task that elicits a detailed set of preference judgments from a single participant in order to evaluate the predictions of several preference learning models from both the inverse decision-making and feature-based classes. [sent-26, score-0.821]

9 Our task requires each participant to sort a large number of observed decisions on the basis of how strongly they indicate 1 (a) (b) (c) d c c (d) b b a a x d x d c b a x 1. [sent-27, score-0.374]

10 Max/min number of effects in a forgone option (+/−) 6. [sent-32, score-0.464]

11 Because the number of decisions is large and these decisions vary on multiple dimensions, predicting how people will order them offers a challenging benchmark on which to compare computational models of preference learning. [sent-49, score-0.932]

12 We then present several inverse decisionmaking and feature-based models of preference learning and compare these models’ predictions to people’s judgments in two experiments. [sent-53, score-0.508]

13 1 Multi-attribute decisions and revealed preferences We designed a task that can be used to elicit a large number of preference judgments from a single participant. [sent-55, score-0.7]

14 Each decision is among a set of options and each option produces a set of effects. [sent-57, score-0.436]

15 Figure 1 shows several decisions involving a total of ﬁve effects distributed among up to ﬁve options. [sent-58, score-0.504]

16 The differently colored boxes represent different effects and the chosen option is marked by a black rectangle. [sent-59, score-0.407]

17 For example, 1a shows a choice between an option with four effects and an option with a single effect; here, the decision maker chose the second option. [sent-60, score-0.811]

18 In our task, people are asked to rank a large number of these decisions by how strongly they suggest that the decision maker had a preference for a particular effect (e. [sent-61, score-0.976]

19 By imposing some minimal constraints, the space of unique multi-attribute decisions is ﬁnite and we can obtain rankings for every decision in the space. [sent-64, score-0.817]

20 If all the effects are positive—pieces of candy, for example—the ﬁrst decision (1a) suggests a strong preference for candy x, because the decision maker turned down four pieces in favor of one. [sent-67, score-1.049]

21 The second decision (1b), however, offers much weaker evidence because nearly everyone would choose four pieces of candy over one, even without a speciﬁc preference for x. [sent-68, score-0.638]

22 When all effects are negative—like electric shocks at different body locations—decision makers may still ﬁnd some effects more tolerable than others, but different inferences are sometimes supported. [sent-70, score-0.702]

23 2 A computational account of preference learning We now describe a simple computational model for learning a person’s preferences after observing that person make a decision like the ones in Figure 1. [sent-72, score-0.581]

24 Let ui denote the utility the decision maker assigns to effect fi . [sent-81, score-0.544]

25 We begin by specifying a model of decision-making that makes the standard assumptions that decision makers tend to choose things with greater utility and that utilities are additive. [sent-82, score-0.53]

26 That is, if fj is a binary vector indicating the effects produced by option oj and u is a vector of utilities assigned to each of the m effects, then the total utility associated with option oj can be expressed as Uj = fj T u. [sent-83, score-0.965]

27 This model can predict the choice someone will make among a speciﬁed set of options, given the utilities that person assigns to the effects in each option. [sent-85, score-0.408]

28 For decisions where effects are positive—like candies—we set µ = 2σ, which corresponds to a prior distribution that places approximately 2% of the probability mass below zero. [sent-93, score-0.504]

29 1 Ordering a set of observed decisions Equation 2 speciﬁes a posterior probability distribution over utilities for a single observed decision but does not provide a way to compare the inferences drawn from multiple decisions for the purposes of ordering them. [sent-96, score-0.849]

30 Suppose we are interested in a decision maker’s preference for effect x and we wish to order a set of decisions by how strongly they support this preference. [sent-97, score-0.74]

31 Two criteria for ordering the decisions are as follows: Absolute utility Relative utility p(c|ux , F)p(ux ) p(c|F) p(c|∀j ux ≥ uj , F)p(∀j ux ≥ uj ) p(∀j ux ≥ uj |c, F) = p(c|F) E(ux |c, F) = Eux The absolute utility model orders decisions by the mean posterior utility for effect x. [sent-98, score-2.176]

32 The relative utility model applies this idea to preference learning by ordering decisions based on how strongly they suggest that x has a greater utility than all other effects. [sent-100, score-1.166]

33 , electric shocks), the absolute utility model predicts that 1b provides stronger evidence for a tolerance for x because the decision maker chose to receive four shocks instead of just one. [sent-104, score-0.821]

34 The relative utility model predicts that 1c provides stronger evidence because 1b offers no way to determine the relative tolerance of the four chosen effects with respect to one another. [sent-105, score-0.667]

35 We assume that the total number of effects is ﬁxed in advance and, as a result, the prior term will be the same for all decisions that we consider. [sent-107, score-0.504]

36 The surprise model captures how unexpected the observed decision is overall; surprising decisions may be best explained in terms of a strong preference for x, but unsurprising decisions provide little information about x in particular. [sent-110, score-1.001]

37 As an example, the ﬁrst feature speciﬁes the number of effects chosen; because x is always among the chosen effects, decisions where few or no other effects belong to the chosen option suggest the strongest preference for x (when all effects are positive). [sent-114, score-1.48]

38 We consider two methods for combining this set of features to order a set of decisions by how strongly they suggest a preference for x. [sent-116, score-0.607]

39 The second model is a ranked feature model that sorts the observed decisions with respect to a strict ranking of the features. [sent-119, score-0.394]

40 For example, suppose that the top-ranked feature is the number of chosen effects and the second-ranked feature is the number of forgone options. [sent-121, score-0.42]

41 This notion of sorting items on the basis of ranked features has been applied before to decision-making [15, 16] and other domains of psychology [17], but we are not aware of any previous applications to preference learning. [sent-123, score-0.481]

42 An inverse decision-making approach may be the appropriate account of preference learning at Marr’s [18] computational level, and a feature-based approach may capture the psychological processes by which the computational-level account is implemented. [sent-125, score-0.542]

43 Finally, the feature-based approach may offer a better account, suggesting that inverse decision-making does not constitute an appropriate computational-level account of preference learning. [sent-130, score-0.466]

44 3 Experiment 1: Positive effects Our ﬁrst experiment focuses on decisions involving only positive effects. [sent-131, score-0.569]

45 dcba | x Figure 2: (a) Comparison between the absolute utility model rankings and the mean human rankings for Experiment 1. [sent-184, score-1.296]

46 (b) Comparison between the mean human rankings in Experiments 1 and 2. [sent-186, score-0.515]

47 (c) The complete set of decisions, ordered by the mean human rankings from Experiment 1. [sent-188, score-0.515]

48 Participants were always asked about a preference for effect x. [sent-190, score-0.331]

49 Participants were told that the effects were different types of candy and each option was a bag containing one or more pieces of candy. [sent-192, score-0.537]

50 They were asked to sort the cards by how strongly each decision suggested that the decision maker liked a particular target candy, labeled x in Figure 2c. [sent-193, score-0.562]

51 They sorted the cards freely on a table but reported their ﬁnal rankings by writing them on a sheet of paper, from weakest to strongest evidence. [sent-194, score-0.491]

52 1 Results Two participants were excluded as outliers based on the criterion that their rankings for at least ﬁve decisions were at least three standard deviations from the mean rankings. [sent-197, score-0.961]

53 We performed a hierarchical clustering analysis of the remaining 41 participants’ rankings using rank correlation as a similarity metric. [sent-198, score-0.41]

54 Participants’ rankings were highly correlated: cutting the resulting dendrogram at 0. [sent-199, score-0.41]

55 2 resulted in one cluster that included 33 participants and the second largest cluster included 5 Surprise MAE = 17. [sent-200, score-0.404]

56 5 Human rankings Experiment 2 Negative effects Representativeness MAE = 2. [sent-205, score-0.647]

57 7 Experiment 1 Positive effects Relative utility MAE = 2. [sent-207, score-0.495]

58 3 Human rankings Absolute utility Model rankings Model rankings Model rankings Model rankings Figure 3: Comparison between human rankings in both experiments and predicted rankings from four models. [sent-208, score-3.238]

59 Because all the effects were positive, we used a prior on utilities that placed nearly all probability mass above zero (µ = 4, σ = 2). [sent-215, score-0.365]

60 The mean human rankings are compared with the absolute utility model rankings in Figure 2a, and the mean human rankings are listed in order in 2c. [sent-216, score-1.811]

61 Fractional rankings were used for both the human data and the model predictions. [sent-217, score-0.489]

62 The human rankings in the ﬁgure are the means of participants’ fractional rankings. [sent-218, score-0.489]

63 Figure 3 shows that the absolute and relative utility models make virtually identical predictions and both models provide a strong account of the human rankings as measured by mean absolute error (MAE = 2. [sent-222, score-1.196]

64 Moreover, both models correctly predict the highest ranked decision and the set of lowest ranked decisions. [sent-224, score-0.347]

65 These are all cases in which effect x appears in all options and therefore these decisions provide no information about a decision maker’s preference for x. [sent-226, score-0.861]

66 Consequently, the models assign the same ranking to this group as to the group of decisions in which there is only a single option (Decisions 1–5). [sent-227, score-0.444]

67 Although people appeared to treat these groups somewhat differently, the models still correctly predict that the entire group of decisions 1–13 is ranked lower than all other decisions. [sent-228, score-0.484]

68 This decision provides no information about a preference for x because it appears in every option. [sent-234, score-0.409]

69 The decision is surprising, however, because a decision maker choosing at random from these options would make the observed choice only 1/4 of the time. [sent-235, score-0.541]

70 The representativeness model performs even worse, primarily because it does not take into account alternative explanations for why an option was chosen, such as the fact that no other options were available (e. [sent-236, score-0.43]

71 The failure of these models to adequately account for the data suggests that both the likelihood p(c|u, F) and marginal likelihood p(c|F) are important components of the absolute and relative utility models. [sent-239, score-0.503]

72 Feature-based models We compared the performance of the absolute and relative utility models to our two feature-based models: the weighted feature and ranked feature models. [sent-240, score-0.68]

73 The histograms show the minimum number of features needed to match the accuracy (measured by MAE) of the absolute utility model for each participant. [sent-242, score-0.413]

74 For the majority of participants, at least four features were needed by both models to match the accuracy of the absolute utility model. [sent-245, score-0.475]

75 For the weighted feature model, 14 participants could not be ﬁt as well as the absolute utility model even when all ten features were considered. [sent-246, score-0.746]

76 4 Experiment 2: Negative effects Experiment 2 focused on a setting in which all effects are negative, motivated by the fact that the inverse decision-making models predict several major differences in orderings when effects are negative rather than positive. [sent-249, score-0.873]

77 For instance, the absolute utility model’s relative rankings of the decisions in Figures 1a and 1b are reversed when all effects are negative rather than positive. [sent-250, score-1.359]

78 The experimental design was identical to Experiment 1 except that participants were told that the effects were electric shocks at different body locations. [sent-252, score-0.669]

79 They were asked to sort the cards on the basis of how strongly each decision suggested that the decision maker ﬁnds shocks at the target location relatively tolerable. [sent-253, score-0.659]

80 The model predictions were derived in the same way as for Experiment 1, but with a prior distribution on utilities that placed nearly all probability mass below zero (µ = −4, σ = 2) to reﬂect the fact that effects were all negative. [sent-254, score-0.399]

81 The resulting mean rankings are compared with the corresponding rankings from Experiment 1 in Figure 2b. [sent-257, score-0.846]

82 Figure 3 shows how the mean rankings compare to the predictions of the four models we considered. [sent-259, score-0.532]

83 Although the relative utility model is fairly accurate, no model achieves the same level of accuracy as the absolute and relative utility models in Experiment 1. [sent-260, score-0.75]

84 In addition, the relative utility model provides a poor account of the responses of many individual participants. [sent-261, score-0.359]

85 To better understand responses at the individual level, we repeated the hierarchical clustering analysis described in Experiment 1, which revealed that 29 participants could be grouped into one of four clusters, with the remaining participants each in their own clusters. [sent-262, score-0.547]

86 We compared the mean rankings of each cluster to the absolute and relative utility models, as well as all one- and two-feature weighted feature and ranked feature models. [sent-264, score-1.127]

87 2 Human rankings Relative utility Cluster 3 N =3 MAE = 2. [sent-274, score-0.668]

88 6 Absolute utility Cluster 2 N = 12 Human rankings Cluster 1 N =8 Factors: 1,3 Factors: 1,8 MAE = 2. [sent-275, score-0.668]

89 2 Model rankings Best−fitting weighted feature Factors: 6,7 MAE = 4. [sent-277, score-0.485]

90 0 Model rankings Model rankings Model rankings Human rankings Factors: 3,8 MAE = 4. [sent-278, score-1.64]

91 8 Figure 5: Comparison between human rankings for four clusters of participants identiﬁed in Experiment 2 and predicted rankings from three models. [sent-279, score-1.214]

92 To examine how well the models accounted for individuals’ rankings within each cluster, we compared the predictions of the inverse decision-making models to the best-ﬁtting two-factor featurebased model for each participant. [sent-283, score-0.608]

93 In Cluster 1, 7 out of 8 participants were best ﬁt by the absolute utility model; in Cluster 2, 8 out of 12 participants were best ﬁt by the relative utility model; in Clusters 3 and 4, all participants were better ﬁt by feature-based models. [sent-284, score-1.448]

94 No single feature-based model provided the best ﬁt for more than two participants, suggesting that participants not ﬁt well by the inverse decision-making models were not using a single alternative strategy. [sent-285, score-0.43]

95 0 features to match the performance of the absolute utility model for participants in Cluster 1, and an average of 3. [sent-287, score-0.671]

96 9 features to match the performance of the relative utility model for participants in Cluster 2. [sent-288, score-0.603]

97 5 Conclusion In two experiments, we found that an inverse decision-making approach offered a good computational account of how people make judgments about others’ preferences. [sent-290, score-0.328]

98 Indeed, the feature-based models that we considered as potential process models of preference learning could only match the performance of the inverse decision-making approach when supplied with a relatively large number of features. [sent-292, score-0.433]

99 However, even if process models that use large numbers of features are considered plausible, the inverse decision-making approach provides a valuable computational-level account that helps to explain which decision features are informative. [sent-295, score-0.413]

100 Dispositional inference from effects of actions: Effects chosen and effects forgone. [sent-391, score-0.498]

similar papers computed by tfidf model

tfidf for this paper:

wordName wordTfidf (topN-words)

[('rankings', 0.41), ('mae', 0.3), ('preference', 0.269), ('decisions', 0.267), ('participants', 0.258), ('utility', 0.258), ('effects', 0.237), ('bax', 0.194), ('options', 0.15), ('ax', 0.147), ('option', 0.146), ('decision', 0.14), ('absolute', 0.113), ('maker', 0.111), ('utilities', 0.104), ('inverse', 0.102), ('people', 0.098), ('shocks', 0.097), ('preferences', 0.092), ('bx', 0.089), ('ranked', 0.088), ('ux', 0.086), ('cards', 0.081), ('candy', 0.081), ('forgone', 0.081), ('human', 0.079), ('representativeness', 0.078), ('cluster', 0.073), ('judgments', 0.072), ('experiment', 0.065), ('psychological', 0.059), ('psychology', 0.058), ('surprise', 0.058), ('logit', 0.057), ('account', 0.056), ('dc', 0.05), ('cbax', 0.048), ('uj', 0.046), ('relative', 0.045), ('participant', 0.044), ('electric', 0.044), ('accounts', 0.043), ('someone', 0.043), ('features', 0.042), ('ordering', 0.04), ('pieces', 0.04), ('cx', 0.04), ('feature', 0.039), ('suggesting', 0.039), ('ac', 0.039), ('infer', 0.038), ('friend', 0.037), ('oj', 0.037), ('weighted', 0.036), ('mellon', 0.035), ('effect', 0.035), ('carnegie', 0.034), ('sort', 0.034), ('predictions', 0.034), ('ab', 0.033), ('told', 0.033), ('bcx', 0.032), ('bdx', 0.032), ('cax', 0.032), ('chatlosh', 0.032), ('dcb', 0.032), ('elek', 0.032), ('hovland', 0.032), ('jern', 0.032), ('four', 0.031), ('rational', 0.031), ('inferences', 0.031), ('models', 0.031), ('correspondence', 0.03), ('others', 0.029), ('negative', 0.029), ('strongly', 0.029), ('makers', 0.028), ('lucas', 0.028), ('comedies', 0.028), ('comedy', 0.028), ('pez', 0.028), ('shepard', 0.028), ('tolerable', 0.028), ('undergraduates', 0.028), ('cognition', 0.028), ('children', 0.027), ('evidence', 0.027), ('asked', 0.027), ('mean', 0.026), ('clusters', 0.026), ('everyone', 0.026), ('osherson', 0.026), ('wilkie', 0.026), ('likes', 0.024), ('sorting', 0.024), ('nearly', 0.024), ('person', 0.024), ('chosen', 0.024), ('perfect', 0.024)]

similar papers list:

simIndex simValue paperId paperTitle

same-paper 1 1.0000001 90 nips-2011-Evaluating the inverse decision-making approach to preference learning

Author: Alan Jern, Christopher G. Lucas, Charles Kemp

2 0.15662009 280 nips-2011-Testing a Bayesian Measure of Representativeness Using a Large Image Database

Author: Joshua T. Abbott, Katherine A. Heller, Zoubin Ghahramani, Thomas L. Griffiths

Abstract: How do people determine which elements of a set are most representative of that set? We extend an existing Bayesian measure of representativeness, which indicates the representativeness of a sample from a distribution, to deﬁne a measure of the representativeness of an item to a set. We show that this measure is formally related to a machine learning method known as Bayesian Sets. Building on this connection, we derive an analytic expression for the representativeness of objects described by a sparse vector of binary features. We then apply this measure to a large database of images, using it to determine which images are the most representative members of different sets. Comparing the resulting predictions to human judgments of representativeness provides a test of this measure with naturalistic stimuli, and illustrates how databases that are more commonly used in computer vision and machine learning can be used to evaluate psychological theories. 1

3 0.14928038 22 nips-2011-Active Ranking using Pairwise Comparisons

Author: Kevin G. Jamieson, Robert Nowak

Abstract: This paper examines the problem of ranking a collection of objects using pairwise comparisons (rankings of two objects). In general, the ranking of n objects can be identiﬁed by standard sorting methods using n log2 n pairwise comparisons. We are interested in natural situations in which relationships among the objects may allow for ranking using far fewer pairwise comparisons. Speciﬁcally, we assume that the objects can be embedded into a d-dimensional Euclidean space and that the rankings reﬂect their relative distances from a common reference point in Rd . We show that under this assumption the number of possible rankings grows like n2d and demonstrate an algorithm that can identify a randomly selected ranking using just slightly more than d log n adaptively selected pairwise comparisons, on average. If instead the comparisons are chosen at random, then almost all pairwise comparisons must be made in order to identify any ranking. In addition, we propose a robust, error-tolerant algorithm that only requires that the pairwise comparisons are probably correct. Experimental studies with synthetic and real datasets support the conclusions of our theoretical analysis. 1

4 0.11412493 15 nips-2011-A rational model of causal inference with continuous causes

Author: Thomas L. Griffiths, Michael James

Abstract: Rational models of causal induction have been successful in accounting for people’s judgments about causal relationships. However, these models have focused on explaining inferences from discrete data of the kind that can be summarized in a 2× 2 contingency table. This severely limits the scope of these models, since the world often provides non-binary data. We develop a new rational model of causal induction using continuous dimensions, which aims to diminish the gap between empirical and theoretical approaches and real-world causal induction. This model successfully predicts human judgments from previous studies better than models of discrete causal inference, and outperforms several other plausible models of causal induction with continuous causes in accounting for people’s inferences in a new experiment. 1

5 0.11274161 34 nips-2011-An Unsupervised Decontamination Procedure For Improving The Reliability Of Human Judgments

Author: Michael C. Mozer, Benjamin Link, Harold Pashler

Abstract: Psychologists have long been struck by individuals’ limitations in expressing their internal sensations, impressions, and evaluations via rating scales. Instead of using an absolute scale, individuals rely on reference points from recent experience. This relativity of judgment limits the informativeness of responses on surveys, questionnaires, and evaluation forms. Fortunately, the cognitive processes that map stimuli to responses are not simply noisy, but rather are inﬂuenced by recent experience in a lawful manner. We explore techniques to remove sequential dependencies, and thereby decontaminate a series of ratings to obtain more meaningful human judgments. In our formulation, the problem is to infer latent (subjective) impressions from a sequence of stimulus labels (e.g., movie names) and responses. We describe an unsupervised approach that simultaneously recovers the impressions and parameters of a contamination model that predicts how recent judgments affect the current response. We test our iterated impression inference, or I3 , algorithm in three domains: rating the gap between dots, the desirability of a movie based on an advertisement, and the morality of an action. We demonstrate signiﬁcant objective improvements in the quality of the recovered impressions. 1

6 0.10296201 52 nips-2011-Clustering via Dirichlet Process Mixture Models for Portable Skill Discovery

7 0.090886809 3 nips-2011-A Collaborative Mechanism for Crowdsourcing Prediction Problems

8 0.087749109 130 nips-2011-Inductive reasoning about chimeric creatures

9 0.083720684 256 nips-2011-Solving Decision Problems with Limited Information

10 0.080477856 35 nips-2011-An ideal observer model for identifying the reference frame of objects

11 0.073004648 88 nips-2011-Environmental statistics and the trade-off between model-based and TD learning in humans

12 0.07080882 122 nips-2011-How Do Humans Teach: On Curriculum Learning and Teaching Dimension

13 0.067336664 20 nips-2011-Active Learning Ranking from Pairwise Preferences with Almost Optimal Query Complexity

14 0.063515037 203 nips-2011-On the accuracy of l1-filtering of signals with block-sparse structure

15 0.051772065 219 nips-2011-Predicting response time and error rates in visual search

16 0.048447076 66 nips-2011-Crowdclustering

17 0.043858234 206 nips-2011-Optimal Reinforcement Learning for Gaussian Systems

18 0.042225312 160 nips-2011-Linear Submodular Bandits and their Application to Diversified Retrieval

19 0.041397907 224 nips-2011-Probabilistic Modeling of Dependencies Among Visual Short-Term Memory Representations

20 0.038331438 154 nips-2011-Learning person-object interactions for action recognition in still images

similar papers computed by lsi model

lsi for this paper:

topicId topicWeight

[(0, 0.125), (1, 0.021), (2, 0.009), (3, 0.055), (4, -0.004), (5, -0.025), (6, -0.026), (7, -0.037), (8, 0.027), (9, 0.057), (10, -0.037), (11, 0.014), (12, 0.047), (13, -0.05), (14, 0.286), (15, -0.031), (16, 0.104), (17, 0.051), (18, 0.161), (19, -0.077), (20, 0.068), (21, -0.021), (22, -0.078), (23, -0.0), (24, -0.079), (25, 0.097), (26, 0.014), (27, -0.103), (28, -0.026), (29, 0.1), (30, -0.022), (31, -0.082), (32, 0.002), (33, 0.06), (34, 0.002), (35, 0.108), (36, -0.088), (37, -0.035), (38, 0.018), (39, 0.013), (40, -0.074), (41, 0.069), (42, 0.095), (43, 0.047), (44, 0.063), (45, -0.052), (46, -0.039), (47, -0.014), (48, -0.058), (49, 0.032)]

similar papers list:

simIndex simValue paperId paperTitle

same-paper 1 0.95631951 90 nips-2011-Evaluating the inverse decision-making approach to preference learning

Author: Alan Jern, Christopher G. Lucas, Charles Kemp

2 0.75664651 34 nips-2011-An Unsupervised Decontamination Procedure For Improving The Reliability Of Human Judgments

Author: Michael C. Mozer, Benjamin Link, Harold Pashler

3 0.74070477 280 nips-2011-Testing a Bayesian Measure of Representativeness Using a Large Image Database

Author: Joshua T. Abbott, Katherine A. Heller, Zoubin Ghahramani, Thomas L. Griffiths

4 0.68152255 122 nips-2011-How Do Humans Teach: On Curriculum Learning and Teaching Dimension

Author: Faisal Khan, Bilge Mutlu, Xiaojin Zhu

Abstract: We study the empirical strategies that humans follow as they teach a target concept with a simple 1D threshold to a robot.1 Previous studies of computational teaching, particularly the teaching dimension model and the curriculum learning principle, offer contradictory predictions on what optimal strategy the teacher should follow in this teaching task. We show through behavioral studies that humans employ three distinct teaching strategies, one of which is consistent with the curriculum learning principle, and propose a novel theoretical framework as a potential explanation for this strategy. This framework, which assumes a teaching goal of minimizing the learner’s expected generalization error at each iteration, extends the standard teaching dimension model and offers a theoretical justiﬁcation for curriculum learning. 1

5 0.62718636 3 nips-2011-A Collaborative Mechanism for Crowdsourcing Prediction Problems

Author: Jacob D. Abernethy, Rafael M. Frongillo

Abstract: Machine Learning competitions such as the Netﬂix Prize have proven reasonably successful as a method of “crowdsourcing” prediction tasks. But these competitions have a number of weaknesses, particularly in the incentive structure they create for the participants. We propose a new approach, called a Crowdsourced Learning Mechanism, in which participants collaboratively “learn” a hypothesis for a given prediction task. The approach draws heavily from the concept of a prediction market, where traders bet on the likelihood of a future event. In our framework, the mechanism continues to publish the current hypothesis, and participants can modify this hypothesis by wagering on an update. The critical incentive property is that a participant will proﬁt an amount that scales according to how much her update improves performance on a released test set. 1

6 0.60605723 15 nips-2011-A rational model of causal inference with continuous causes

7 0.57933915 130 nips-2011-Inductive reasoning about chimeric creatures

8 0.49311686 35 nips-2011-An ideal observer model for identifying the reference frame of objects

9 0.41262916 22 nips-2011-Active Ranking using Pairwise Comparisons

10 0.4124521 52 nips-2011-Clustering via Dirichlet Process Mixture Models for Portable Skill Discovery

11 0.3362923 20 nips-2011-Active Learning Ranking from Pairwise Preferences with Almost Optimal Query Complexity

12 0.32042697 194 nips-2011-On Causal Discovery with Cyclic Additive Noise Models

13 0.30810684 42 nips-2011-Bayesian Bias Mitigation for Crowdsourcing

14 0.30510327 219 nips-2011-Predicting response time and error rates in visual search

15 0.30462664 60 nips-2011-Confidence Sets for Network Structure

16 0.30361921 256 nips-2011-Solving Decision Problems with Limited Information

17 0.30248621 66 nips-2011-Crowdclustering

18 0.29169956 11 nips-2011-A Reinforcement Learning Theory for Homeostatic Regulation

19 0.28990075 120 nips-2011-History distribution matching method for predicting effectiveness of HIV combination therapies

20 0.28114107 293 nips-2011-Understanding the Intrinsic Memorability of Images

similar papers computed by lda model

lda for this paper:

topicId topicWeight

[(4, 0.071), (20, 0.025), (26, 0.023), (27, 0.019), (31, 0.113), (33, 0.025), (39, 0.011), (43, 0.06), (45, 0.086), (56, 0.017), (57, 0.051), (65, 0.012), (74, 0.041), (83, 0.044), (84, 0.011), (97, 0.288), (99, 0.029)]

similar papers list:

simIndex simValue paperId paperTitle

1 0.78341514 184 nips-2011-Neuronal Adaptation for Sampling-Based Probabilistic Inference in Perceptual Bistability

Author: David P. Reichert, Peggy Series, Amos J. Storkey

Abstract: It has been argued that perceptual multistability reﬂects probabilistic inference performed by the brain when sensory input is ambiguous. Alternatively, more traditional explanations of multistability refer to low-level mechanisms such as neuronal adaptation. We employ a Deep Boltzmann Machine (DBM) model of cortical processing to demonstrate that these two different approaches can be combined in the same framework. Based on recent developments in machine learning, we show how neuronal adaptation can be understood as a mechanism that improves probabilistic, sampling-based inference. Using the ambiguous Necker cube image, we analyze the perceptual switching exhibited by the model. We also examine the inﬂuence of spatial attention, and explore how binocular rivalry can be modeled with the same approach. Our work joins earlier studies in demonstrating how the principles underlying DBMs relate to cortical processing, and offers novel perspectives on the neural implementation of approximate probabilistic inference in the brain. 1

same-paper 2 0.76612139 90 nips-2011-Evaluating the inverse decision-making approach to preference learning

Author: Alan Jern, Christopher G. Lucas, Charles Kemp

3 0.6461516 10 nips-2011-A Non-Parametric Approach to Dynamic Programming

Author: Oliver B. Kroemer, Jan R. Peters

Abstract: In this paper, we consider the problem of policy evaluation for continuousstate systems. We present a non-parametric approach to policy evaluation, which uses kernel density estimation to represent the system. The true form of the value function for this model can be determined, and can be computed using Galerkin’s method. Furthermore, we also present a uniﬁed view of several well-known policy evaluation methods. In particular, we show that the same Galerkin method can be used to derive Least-Squares Temporal Diﬀerence learning, Kernelized Temporal Diﬀerence learning, and a discrete-state Dynamic Programming solution, as well as our proposed method. In a numerical evaluation of these algorithms, the proposed approach performed better than the other methods. 1

4 0.54679239 75 nips-2011-Dynamical segmentation of single trials from population neural data

Author: Biljana Petreska, Byron M. Yu, John P. Cunningham, Gopal Santhanam, Stephen I. Ryu, Krishna V. Shenoy, Maneesh Sahani

Abstract: Simultaneous recordings of many neurons embedded within a recurrentlyconnected cortical network may provide concurrent views into the dynamical processes of that network, and thus its computational function. In principle, these dynamics might be identiﬁed by purely unsupervised, statistical means. Here, we show that a Hidden Switching Linear Dynamical Systems (HSLDS) model— in which multiple linear dynamical laws approximate a nonlinear and potentially non-stationary dynamical process—is able to distinguish different dynamical regimes within single-trial motor cortical activity associated with the preparation and initiation of hand movements. The regimes are identiﬁed without reference to behavioural or experimental epochs, but nonetheless transitions between them correlate strongly with external events whose timing may vary from trial to trial. The HSLDS model also performs better than recent comparable models in predicting the ﬁring rate of an isolated neuron based on the ﬁring rates of others, suggesting that it captures more of the “shared variance” of the data. Thus, the method is able to trace the dynamical processes underlying the coordinated evolution of network activity in a way that appears to reﬂect its computational role. 1

5 0.52785826 219 nips-2011-Predicting response time and error rates in visual search

Author: Bo Chen, Vidhya Navalpakkam, Pietro Perona

Abstract: A model of human visual search is proposed. It predicts both response time (RT) and error rates (RT) as a function of image parameters such as target contrast and clutter. The model is an ideal observer, in that it optimizes the Bayes ratio of target present vs target absent. The ratio is computed on the ﬁring pattern of V1/V2 neurons, modeled by Poisson distributions. The optimal mechanism for integrating information over time is shown to be a ‘soft max’ of diffusions, computed over the visual ﬁeld by ‘hypercolumns’ of neurons that share the same receptive ﬁeld and have different response properties to image features. An approximation of the optimal Bayesian observer, based on integrating local decisions, rather than diffusions, is also derived; it is shown experimentally to produce very similar predictions to the optimal observer in common psychophysics conditions. A psychophyisics experiment is proposed that may discriminate between which mechanism is used in the human brain. A B C Figure 1: Visual search. (A) Clutter and camouﬂage make visual search difﬁcult. (B,C) Psychologists and neuroscientists build synthetic displays to study visual search. In (B) the target ‘pops out’ (∆θ = 450 ), while in (C) the target requires more time to be detected (∆θ = 100 ) [1]. 1

6 0.52685577 180 nips-2011-Multiple Instance Filtering

7 0.52592933 229 nips-2011-Query-Aware MCMC

8 0.52158195 192 nips-2011-Nonstandard Interpretations of Probabilistic Programs for Efficient Inference

9 0.51980054 140 nips-2011-Kernel Embeddings of Latent Tree Graphical Models

10 0.51919061 206 nips-2011-Optimal Reinforcement Learning for Gaussian Systems

11 0.51740646 258 nips-2011-Sparse Bayesian Multi-Task Learning

12 0.51695317 273 nips-2011-Structural equations and divisive normalization for energy-dependent component analysis

13 0.51625085 139 nips-2011-Kernel Bayes' Rule

14 0.51613784 37 nips-2011-Analytical Results for the Error in Filtering of Gaussian Processes

15 0.51527822 55 nips-2011-Collective Graphical Models

16 0.51512063 57 nips-2011-Comparative Analysis of Viterbi Training and Maximum Likelihood Estimation for HMMs

17 0.5150708 301 nips-2011-Variational Gaussian Process Dynamical Systems

18 0.5149045 86 nips-2011-Empirical models of spiking in neural populations

19 0.51472056 241 nips-2011-Scalable Training of Mixture Models via Coresets

20 0.51380605 66 nips-2011-Crowdclustering