acl acl2010 acl2010-13 knowledge-graph by maker-knowledge-mining

13 acl-2010-A Rational Model of Eye Movement Control in Reading

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Author: Klinton Bicknell ; Roger Levy

Abstract: A number of results in the study of realtime sentence comprehension have been explained by computational models as resulting from the rational use of probabilistic linguistic information. Many times, these hypotheses have been tested in reading by linking predictions about relative word difficulty to word-aggregated eye tracking measures such as go-past time. In this paper, we extend these results by asking to what extent reading is well-modeled as rational behavior at a finer level of analysis, predicting not aggregate measures, but the duration and location of each fixation. We present a new rational model of eye movement control in reading, the central assumption of which is that eye move- ment decisions are made to obtain noisy visual information as the reader performs Bayesian inference on the identities of the words in the sentence. As a case study, we present two simulations demonstrating that the model gives a rational explanation for between-word regressions.

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Summary: the most important sentenses genereted by tfidf model

sentIndex sentText sentNum sentScore

1 edu Abstract A number of results in the study of realtime sentence comprehension have been explained by computational models as resulting from the rational use of probabilistic linguistic information. [sent-3, score-0.292]

2 Many times, these hypotheses have been tested in reading by linking predictions about relative word difficulty to word-aggregated eye tracking measures such as go-past time. [sent-4, score-0.586]

3 In this paper, we extend these results by asking to what extent reading is well-modeled as rational behavior at a finer level of analysis, predicting not aggregate measures, but the duration and location of each fixation. [sent-5, score-0.557]

4 We present a new rational model of eye movement control in reading, the central assumption of which is that eye move- ment decisions are made to obtain noisy visual information as the reader performs Bayesian inference on the identities of the words in the sentence. [sent-6, score-1.509]

5 As a case study, we present two simulations demonstrating that the model gives a rational explanation for between-word regressions. [sent-7, score-0.416]

6 To the extent that the behavior of these models looks like human behavior, it suggests that humans are making rational use of all the information available to them in language processing. [sent-14, score-0.3]

7 In this paper, we present a new rational model of eye movement control in reading, the central assumption of which is that eye movement decisions are made to obtain noisy visual informa- tion, which the reader uses in Bayesian inference about the form and structure of the sentence. [sent-25, score-1.581]

8 As a case study, we show that this model gives a rational explanation for between-word regressions. [sent-26, score-0.352]

9 In Section 2, we briefly describe the leading models of eye movements in reading, and in Section 3, we describe how these models account for between-word regressions and the intuition behind our model’s account of them. [sent-27, score-0.495]

10 Section 4 describes the model and its implementation and Sections 5– 6 describe two simulations we performed with the model comparing behavioral policies that make regressions to those that do not. [sent-28, score-0.509]

11 In Simulation 1, we show that specific regressive policies outperform specific non-regressive policies, and in Simulation 2, we use optimization to directly find optimal policies for three performance measures. [sent-29, score-0.458]

12 The results show that the regressive policies outperform non-regressive policies across a wide range of performance measures, demonstrating that our model predicts that making between-word regressions is a rational strategy for reading. [sent-30, score-0.919]

13 2 Models of eye movements in reading The two most successful models of eye movements in reading are E-Z Reader (Reichle, Pollatsek, Fisher, & Rayner, 1998; Reichle et al. [sent-31, score-1.12]

14 While both of these models provide a good fit to eye tracking data from reading, neither model asks the higher level question of what a rational solution to the problem would look like. [sent-37, score-0.568]

15 Chips model simplifies the problem of reading in a number of ways: First, it uses a unigram model as its language model, and thus fails to use any information in the linguistic context to help with word identification. [sent-41, score-0.379]

16 The larger problem, however, is that each of these models uses an unrealistic model of visual input, which obtains absolute knowledge of the characters in its visual window. [sent-45, score-0.744]

17 Thus, there is no reason for the model to spend longer on one fixation than another, and the model only makes predictions for where saccades are targeted, and not how long fixations last. [sent-46, score-0.408]

18 Reichle and Laurent (2006) presented a rational model that overcame the limitations of Mr. [sent-47, score-0.315]

19 Chips to produce predictions for both fixation durations and locations, focusing on the ways in which eye movement behavior is an adaptive response to the particular constraints of the task of reading. [sent-48, score-0.549]

20 In this paper, we present another rational model of eye movement control in reading that, like Reichle and Laurent, makes predictions for fixation durations and locations, but which focuses instead on the dynamics of word identification at the core of the task of reading. [sent-50, score-1.16]

21 Specifically, our model identifies the words in a sentence by performing Bayesian inference combining noisy input from a realistic visual model with a language model that takes context into account. [sent-51, score-0.664]

22 3 Explaining between-word regressions In this paper, we use our model to provide a novel explanation for between-word regressive saccades. [sent-52, score-0.44]

23 In reading, about 10–15% of saccades are regressive movements from right-to-left (or to previous lines). [sent-53, score-0.325]

24 , the eyes move backwards to a previous word because they accidentally landed further forward than intended due to motor error. [sent-59, score-0.312]

25 From the present perspective, however, it is unclear how it could be rational to move past an unidentified word and decide to revisit it only much later. [sent-67, score-0.338]

26 – Here, we suggest – a new explanation for between-word regressions that arises as a result of word identification processes (unlike that of E-Z Reader) and can be understood as rational (unlike that of SWIFT). [sent-68, score-0.516]

27 Thus, it is possible that later parts of a sentence can cause a reader’s confidence in the identity of the previous regions to fall. [sent-70, score-0.352]

28 In these cases, a rational way to respond might be to make a between-word regressive saccade to get more visual information about the (now) low confidence previous region. [sent-71, score-0.921]

29 To illustrate this idea, consider the case of a language composed of just two strings, AB and BA, and assume that the eyes can only get noisy in- formation about the identity of one character at a time. [sent-72, score-0.529]

30 After obtaining a little information about the identity of the first character, the reader may be reasonably confident that its identity is A and move on to obtaining visual input about the second character. [sent-73, score-0.933]

31 If the first noisy input about the second character also indicates that it is probably A, then the normative probability that the first character is A (and thus a rational reader’s confidence in its identity) will fall. [sent-74, score-0.732]

32 This simple example just illustrates the point that if a reader is combining noisy visual information with a language model, then confidence in previous regions will sometimes fall. [sent-75, score-0.682]

33 The second option is to read left-to-right relatively more quickly, and then make occasional right-to-left regressions in the cases where probability in previous regions falls. [sent-80, score-0.312]

34 In this paper, we present two simulations suggesting that when using a rational model to read natural language, the best strategies for coping with the problem of confidence about previous regions dropping for any tradeoff between speed and accuracy involve making between-word regressions. [sent-81, score-0.615]

35 In the next section, we present the details of our model of reading and its implementation, and then we present our two simulations in the sections following. [sent-82, score-0.382]

36 Specifically, the model begins reading with a prior distribution over possible identities of a sentence given by its language model. [sent-84, score-0.409]

37 On the basis of that distribution, the model decides whether or not to move its eyes (and if so where to move them to) and obtains noisy visual input about the sentence at the eyes’ position. [sent-85, score-0.878]

38 This framework is unique among models of eye movement control in reading (except Mr. [sent-88, score-0.652]

39 Chips) in having a fully explicit model of how visual input is used to discriminate word identity. [sent-89, score-0.445]

40 The hope in our approach is that the influence of these key factors on the eye movement record will fall out as a natural consequence of rational behavior itself. [sent-91, score-0.643]

41 In our framework, in contrast, we would expect such an effect to emerge as a byproduct of Bayesian inference: words with high prior probability (conditional on preceding fixations) will require less visual input to be reliably identified. [sent-94, score-0.384]

42 In the remainder of this section, we present these details of the formalization of the reading problem we used for the simulations reported in this paper: actions (4. [sent-96, score-0.368]

43 If on the ith timestep, the model chooses option (a), the timestep advances to i+ 1 and another sample of visual input is obtained around the current position. [sent-104, score-0.52]

44 If the model chooses option (c), the reading immediately ends. [sent-105, score-0.318]

45 On the next time step, visual input is obtained around ‘i and another decision is made. [sent-107, score-0.384]

46 The motor error for sac– – cades follows the form of random error used by all major models of eye movements in reading: the landing position ‘i is normally distributed around the intended target ti with standard deviation given by a linear function of the intended distance1 ‘i ∼ N ? [sent-108, score-0.425]

47 2 Noisy visual input As stated earlier, the role of noisy visual input in our model is as the likelihood term in a Bayesian inference about sentence form and identity. [sent-117, score-0.926]

48 r Wacete ars position are conditionally independent given sentence identity, so that if wj denotes letter j of the sen- tence and I(j) denotes the component of visual input a anssdoc Ii(atje)d weintoht ethsa tht letter, pthoenne we can duae-l compose p(I|w) as ∏jp(I(j) |wj). [sent-120, score-0.691]

49 The visual input obtained from an individual fixation can thus be summarized a vector of likelihoods p(I(j) |wj), as as shown in 1In the terminology of the literature, the model has only random motor error (variance), not systematic error (bias). [sent-122, score-0.622]

50 0 4  Figure 1: Peripheral and foveal visual input in the model. [sent-151, score-0.474]

51 In peripheral vision, the letter/whitespace distinction is veridical, but no information about letter identity is obtained. [sent-155, score-0.38]

52 As in the real visual system, our vi- sual acuity function decreases with retinal eccentricity; we follow the SWIFT model in assuming that the spatial distribution of visual processing rate follows an asymmetric Gaussian with σL = 2. [sent-158, score-0.781]

53 If ε denotes a character’s eccentricity in characters from the center of fixation, then the proportion of the total processing rate at that eccentricity λ (ε) is given by integrating the asymmetric Gaussian over a character width centered on that position, λ(ε) =Zε−ε+. [sent-161, score-0.369]

54 From this distribution, we derive two types of visual input, peripheral input giving word boundary information and foveal input giving information about letter identity. [sent-166, score-0.754]

55 1 Peripheral visual input In our model, any eccentricity with a processing rate proportion λ (ε) at least 0. [sent-169, score-0.501]

56 5% of the rate proportion for the centrally fixated character (ε ∈ [−7, 12]), yields peripheral xvaitseudal input, edref (iεne ∈d as 7v,e1ri2d]i),ca yl ewldosrd p boundary viinsfuoarlm iantpiount, i dnedfiincaetding whether each character is a letter or a space. [sent-170, score-0.598]

57 This roughly corresponds to empirical estimates that humans obtain useful information in reading from about 19 characters, more from the right of fixation than the left (Rayner, 1998). [sent-171, score-0.374]

58 Hence in Figure 1, for example, left-peripheral visual input can be represented as veridical knowledge ofthe initial whitespace (denoted d ), and a uniform distribution over the 26 letters of English for the letter a. [sent-172, score-0.525]

59 This threshold of 1% roughly corresponds to estimates that readers get information useful for letter identification from about 4 characters to the left and 8 to the right of fixation (Rayner, 1998). [sent-176, score-0.326]

60 In our model, each letter is equally confusable with all others, following Norris (2006, 2009), but ignoring work on letter confusability (which could be added to future model revisions; Engel, Dougherty, & Jones, 1973; Geyer, 1977). [sent-177, score-0.373]

61 (3) If the eccentricity of the jth character on the tth timestep is outside of foveal input or the character is a space, the inner term is 0 or 1. [sent-189, score-0.584]

62 If the sample was from a letter in foveal input ∈ [−5, 8], it is the probability of sampling It (j) fro∈m[ −th5e, m8],u iltitisva thriea tper oGbaabusilsi tayn o N(wj, ΛΣ(εtj)). [sent-190, score-0.291]

63 4 Control policy The model uses a simple policy to decide between actions based on the marginal probability m of the (a) m = [. [sent-192, score-0.404]

64 7] : Stop reading Figure 2: Values of m for a 6 character sentence under which a model fixating position 3 would take each of its four actions, if α = . [sent-216, score-0.608]

65 If the value of this statistic for the current position of the eyes m(‘i) is less than a parameter α, the model chooses to continue fixating the current position (2a). [sent-222, score-0.401]

66 Otherwise, if the value of m(j) is less than β for some leftward position j < ‘i, the model initiates a saccade to the closest such position (2b). [sent-223, score-0.303]

67 3 Finally, if no such positions exist to the right, the model stops reading the sentence (2d). [sent-226, score-0.356]

68 Intuitively, then, the model reads by making a rightward sweep to bring its confidence in each character up to α, but pauses to move left if confidence in a previous character falls below β . [sent-227, score-0.579]

69 To perform belief update given a new visual input, we create a new wFSA to represent the likelihood of each character from the sample. [sent-230, score-0.498]

70 , the first and second state in the chain are connected by 27 (or fewer) arcs, which emit each of 3The role of n is to ensure that the model does not center its visual field on the first uncertain character. [sent-233, score-0.385]

71 1173 the possible characters for w1 along with their respective likelihoods given the visual input (as in the inner term of Equation 3). [sent-235, score-0.419]

72 5 Simulation 1 With the description of our model in place, we next proceed to describe the first simulation in which we used the model to test the hypothesis that making regressions is a rational way to cope with confidence in previous regions falling. [sent-238, score-0.807]

73 In the terms of our model’s policy parameters α and β described above, non-regressive policies are exactly those with β = 0, and a policy that is faster on the left-to-right pass but does make regressions is one with a lower value of α but a non-zero β . [sent-240, score-0.619]

74 Thus, we tested the performance of our model on the reading of a corpus of text typical of that used in reading experiments at a range of reasonable non-regressive policies, as well as a set of regressive policies with lower α and positive β . [sent-241, score-0.856]

75 This was done in order to facilitate simple composition with the visual likelihood wFSA defined over characters. [sent-275, score-0.324]

76 2 Results and discussion For each policy we tested, we measured the average number of timesteps it took to read the sentences, as well as the average (natural) log probability of the correct sentence identity under the model’s beliefs after reading ended ‘Accuracy’ . [sent-285, score-0.829]

77 As shown in the graph, for each non-regressive policy (the circles), there is a regressive policy that outperforms it, both in terms of average number of timesteps taken to read (further to the left) and the average log probability of the sentence identity (higher). [sent-287, score-0.87]

78 Thus, for a range of policies, these results suggest 1174 Timesteps Figure 3: Mean number of timesteps taken to read a sentence and (natural) log probability of the true identity of the sentence ‘Accuracy’ for a range of values of α and β . [sent-288, score-0.495]

79 For each non-regressive policy (β = 0), there is a policy with a lower α and higher β that achieves better accuracy in less time. [sent-290, score-0.296]

80 that making regressions when confidence about previous regions falls is a rational reader strategy, in that it appears to lead to better performance, both in terms of speed and accuracy. [sent-291, score-0.786]

81 6 Simulation 2 In Simulation 2, we perform a more direct test of the idea that making regressions is a rational response to the problem of confidence falling about previous regions using optimization techniques. [sent-292, score-0.6]

82 2 Optimization of policy parameters Searching directly for optimal values of α and β for our stochastic reading model is difficult because each evaluation of the model with a particular set of parameters produces a different result. [sent-308, score-0.606]

83 In addition, we see that the average results of reading at these parameter values are also as we would expect, with T and L going up as γ goes down. [sent-341, score-0.29]

84 This provides more evidence that whatever the particular performance measure used, policies making regressive saccades when confidence in previous regions falls perform better than those that do not. [sent-361, score-0.525]

85 That may at first seem surprising, since the model’s policy is to fixate a region until its confidence becomes greater than α and then return if it falls below β . [sent-364, score-0.259]

86 7 Conclusion In this paper, we presented a model that performs Bayesian inference on the identity of a sentence, combining a language model with noisy information about letter identities from a realistic visual input model. [sent-369, score-0.919]

87 On the basis of these inferences, it uses a simple policy to determine how long to continue fixating the current position and where to fixate next, on the basis of information about where the model is uncertain about the sentence’s identity. [sent-370, score-0.355]

88 As such, it constitutes a rational model of eye movement control in reading, extending the insights from previous results about rationality in language comprehension. [sent-371, score-0.71]

89 The results of two simulations using this model support a novel explanation for between-word regressive saccades in reading: that they are used to gather visual input about previous regions when confidence about them falls. [sent-372, score-0.94]

90 Rational eye movements in reading combining uncertainty about previous words with contextual probability. [sent-403, score-0.596]

91 Parsing costs as predictors of reading difficulty: An evaluation using the potsdam sentence corpus. [sent-414, score-0.295]

92 Contextual effects on word perception and eye movements during reading. [sent-433, score-0.303]

93 A dynamical model of saccade generation in reading based on spatially distributed lexical processing. [sent-444, score-0.436]

94 A noisy-channel model of rational human sentence comprehension under uncertain input. [sent-542, score-0.353]

95 A Bayesian model predicts human parse preference and reading time in sentence processing. [sent-585, score-0.356]

96 Eye movements in reading and information processing: 20 years of research. [sent-610, score-0.342]

97 Toward a model of eye movement control in reading. [sent-626, score-0.456]

98 Using E-Z Reader to model the effects of higher level language processing on eye movements during reading. [sent-640, score-0.364]

99 Comparing naming, lexical decision, and eye fixation times: Word frequency effects and individual differences. [sent-649, score-0.335]

100 Integration of visual and linguistic information in spoken language comprehension. [sent-674, score-0.324]

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