nips nips2002 nips2002-71 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Aaron J. Gruber, Sara A. Solla, James C. Houk
Abstract: Single unit activity in the striatum of awake monkeys shows a marked dependence on the expected reward that a behavior will elicit. We present a computational model of spiny neurons, the principal neurons of the striatum, to assess the hypothesis that direct neuromodulatory effects of dopamine through the activation of D 1 receptors mediate the reward dependency of spiny neuron activity. Dopamine release results in the amplification of key ion currents, leading to the emergence of bistability, which not only modulates the peak firing rate but also introduces a temporal and state dependence of the model's response, thus improving the detectability of temporally correlated inputs. 1
Reference: text
sentIndex sentText sentNum sentScore
1 edu Abstract Single unit activity in the striatum of awake monkeys shows a marked dependence on the expected reward that a behavior will elicit. [sent-5, score-0.208]
2 We present a computational model of spiny neurons, the principal neurons of the striatum, to assess the hypothesis that direct neuromodulatory effects of dopamine through the activation of D 1 receptors mediate the reward dependency of spiny neuron activity. [sent-6, score-1.584]
3 Dopamine release results in the amplification of key ion currents, leading to the emergence of bistability, which not only modulates the peak firing rate but also introduces a temporal and state dependence of the model's response, thus improving the detectability of temporally correlated inputs. [sent-7, score-0.332]
4 For instance, striatal activity related to visual stimuli is dependent on the type of reinforcement (primary vs secondary) that a behavior will elicit [1]. [sent-10, score-0.156]
5 Task-related activity can be enhanced or suppressed when a reward is anticipated for correct performance, relative to activity when no reward is expected. [sent-11, score-0.408]
6 Although the origin of this reward dependence has not been experimentally verified, dopamine modulation is likely to playa role. [sent-12, score-0.588]
7 Spiny neurons in the striatum, the input to the basal ganglia, receive a prominent neuromodulatory input from dopamine neurons in the substantia nigra pars compacta. [sent-13, score-0.772]
8 These dopamine neurons discharge in a rewarddependent manner [2]; they respond to the delivery of unexpected rewards and to sensory cues that reliably precede the delivery of expected rewards. [sent-14, score-0.652]
9 Activation of dopamine receptors alters the response characteristics of spiny neurons by modulating the properties of voltage-gated ion channels, as opposed to simple excitatory or inhibitory effects [3]. [sent-15, score-1.131]
10 Activation of the D1 type dopamine receptor alone can either enhance or suppress neural responses depending on the prior state of the spiny neuron [4]. [sent-16, score-1.087]
11 Here, we use a computational approach to assess the hypothesis that the modulation of specific ion channels through the activation of D1 receptors is sufficient to explain both the enhanced and suppressed single unit responses of medium spiny neurons to reward-predicting stimuli. [sent-17, score-0.92]
12 We have constructed a biophysically grounded model of a spiny neuron and used it to investigate whether dopamine neuromodulation accounts for the observed rewarddependence of striatal single-unit responses to visual targets in the memory guided saccade task described by [1]. [sent-18, score-1.059]
13 These authors used an asymmetric reward schedule and compared the response to a given target in rewarded as opposed to unrewarded cases. [sent-19, score-0.323]
14 They report a substantial reward-dependent difference; the majority of these neurons showed a reward-related enhancement of the intensity and duration of discharge, and a smaller number exhibited a reward-related depression. [sent-20, score-0.17]
15 The authors speculated that D1 receptor activation might account for enhanced responses, whereas D2 receptor activation might explain the depressed responses. [sent-21, score-0.405]
16 The model presented here demonstrates that neuromodulatory actions of dopamine through D1 receptors suffice to account for both effects, with interesting consequences for information processing. [sent-22, score-0.574]
17 2 Model description The membrane properties of the model neuron result from an accurate representation of a minimal set of currents needed to reproduce the characteristic behavior of spiny neurons. [sent-23, score-0.68]
18 In low dopamine conditions, these cells exhibit quasi two-state behavior; they spend most of their time either in a hyperpolarized 'down' state around -85 mV, or in a depolarized 'up' state around -55 mV [5]. [sent-24, score-0.798]
19 This bimodal character of the response to cortical input is attributed to a combination of inward rectifying (IRK) and outward rectifying (ORK) potassium currents [5]. [sent-25, score-0.364]
20 IRK contributes a small outward current at hyperpolarized membrane potentials, thus providing resistance to depolarization and stabilizing the down state. [sent-26, score-0.309]
21 ORK is a major hyperpolarizing current that becomes activated at depolarized potentials and opposes the depolarizing influences of excitatory synaptic and inward ionic currents; it is their balance that determines the membrane potential of the up state. [sent-27, score-0.67]
22 In addition to IRK and ORK currents, the model incorporates the L-type calcium (L-Ca) current that starts to provide an inward current at subthreshold membrane potentials, thus determining the voltage range of the up state. [sent-28, score-0.297]
23 This current has the ability to increase the firing rate of spiny neurons and is critical to the enhancement of spiny neuron responses in the presence of D1 agonists [4]. [sent-29, score-1.031]
24 Our goal is to design a model that provides a consistent description of membrane properties in the 100 - 1000 ms time range. [sent-30, score-0.138]
25 This is the characteristic range of duration for up and down state episodes; it also spans the time course of short term modulatory effects of dopamine. [sent-31, score-0.143]
26 Thus, the model does not incorporate currents which inactivate on a short time scale, and cannot provide a good description of rapid events such as the transitions between up and down states or the generation of action potentials. [sent-33, score-0.147]
27 The membrane of a spiny neuron is modeled here as a single compartment with steady-state voltage-gated ion currents. [sent-34, score-0.646]
28 A first order differential equation relates the temporal change in membrane potential (Vm ) to the membrane currents (Ii), (1) The right hand side of the equation includes active ionic, leakage, and synaptic currents. [sent-35, score-0.555]
29 The multiplicative factor 'Y models the modulatory effects of D1 receptor activation by dopamine, to be described in more detail later. [sent-36, score-0.237]
30 Ionic currents are modeled using a standard formulation; the parameters are as reported in the biophysical literature, except for adjustments that compensate for specific experimental conditions so as to more closely match in vivo realizations. [sent-37, score-0.215]
31 All currents except for L-Ca are modeled by the product of a voltage gated conductance and a linear driving force , Ii = gi (Vm - E i ), where Ei is the reversal potential of ion species i and gi is the corresponding conductance. [sent-38, score-0.469]
32 hLi (Vm ), where 9i is the maximum conductance and Li (Vm ) is a logistic function of the membrane potential. [sent-40, score-0.237]
33 The resulting ionic currents are shown in Fig 1A. [sent-42, score-0.242]
34 The synaptic current is modeled as the product of a conductance and a linear driving force, 18 = g8(Vm - E 8), with E8 = O. [sent-43, score-0.284]
35 The synaptic conductance includes two types of cortical input: a phasic sensory-related component gp, and a tonic context-related component gt, which are added to determine the total synaptic input: g8 = ~(gp + gt). [sent-44, score-0.459]
36 Dopamine modulates the properties of ion currents though the activation of specific receptors. [sent-46, score-0.401]
37 Agonists for the D1 type receptor enhance the IRK and L-Ca currents observed in spiny neurons [7, 8]. [sent-47, score-0.697]
38 0 corresponds to low dopamine levels; this is the experimental condition in which the ion currents have been characterized. [sent-52, score-0.701]
39 At low dopamine levels, Vm is a single-valued monotonically increasing function of g8, shown in Fig 1B (dotted line). [sent-57, score-0.471]
40 This operational curve describes a A B -30 2 >-50 N E () ::c 0 +--1----=::::::__ . [sent-58, score-0.19]
41 gradual, smooth transition from hyperpolarized values of Vm corresponding to the down state to depolarized values of Vm corresponding to the up state. [sent-74, score-0.273]
42 4), the membrane potential is a single-valued monotonically increasing function of the synaptic conductance for either g8 < 9. [sent-76, score-0.369]
43 The resulting operational curve, shown Fig 1B (solid line), consists of three branches: two stable and one unstable. [sent-82, score-0.185]
44 The two stable branches (dark solid lines) correspond to a hyperpolarized down state (lower branch) and a depolarized up state (upper branch). [sent-83, score-0.437]
45 Bistability arises through a saddle node bifurcation with increasing 'Y and has a drastic effect on the response properties of the model neuron in high dopamine conditions. [sent-85, score-0.628]
46 4 and g8 changes slowly so as to allow Vm to follow its equilibrium value on the operational curve for 'Y = 1. [sent-87, score-0.227]
47 As g8 increases, the hyperpolarized down state follows the lower stable branch. [sent-89, score-0.184]
48 17 JLS/cm 2 , the synaptic current suddenly overcomes the mostly IRK hyperpolarizing current, and Vm depolarizes abruptly to reach an up state stabilized by the activation of the hyperpolarizing aRK current. [sent-91, score-0.448]
49 If g8 is now decreased, the depolarized up state follows the stable upper branch in the downward direction. [sent-94, score-0.294]
50 It is the inward L-Ca current which counteracts the hyperpolarizing effect of the aRK current and stabilizes the up state until g8 reaches 9. [sent-95, score-0.296]
51 74 JLS/cm 2 , where a net hyperpolarizing ionic current overtakes the system and Vm hyperpolarizes abruptly to the down state. [sent-96, score-0.273]
52 The emergence of bistability in high dopamine conditions results in a prominent hysteresis effect. [sent-98, score-0.593]
53 The state of the model, as described by the value of Vm , depends not only on the current values of 'Y and g8' but also on the particular trajectory followed by these parameters to reach their current values. [sent-99, score-0.126]
54 The appearance of bistability gives a well defined meaning to the notion of a down state and an up state: in this case there is a gap between the two stable branches, while in low dopamine conditions the transition is smooth, with no clear separation between states. [sent-100, score-0.683]
55 We generically refer to hyperpolarized potentials as the down state and depolarized potentials as the up state, for consistency with the electrophysiological terminology. [sent-101, score-0.333]
56 tS/cm2) Figure 2: Response to a sensory related phasic input in rewarded and unrewarded trials. [sent-188, score-0.361]
57 An important feature of the model is that operational curves for all values of, intersect at a unique point, indicated by a circle in Fig 1B, for which V;' = - 55. [sent-190, score-0.149]
58 The existence of a critical point at a slightly more depolarized membrane potential than the firing threshold at VI = - 58 m V is an important aspect of our model; it plays a role in the mechanism that allows dopamine to either enhance or depress the response of the model spiny neuron. [sent-195, score-1.295]
59 Consider a scenario in which a tonic input gt maintains Vm below VI; the response to an additional phasic input gp sufficient to drive Vm above VI depends on whether it is associated with expected reward and thus triggers dopamine release. [sent-197, score-1.143]
60 The response of the model neuron depends on the combined synaptic input g8 in a manner that is critically dependent on the expectation of reward. [sent-198, score-0.253]
61 If the phasic input is not associated with reward, the dopamine level does not increase (left panels in Fig 2). [sent-200, score-0.656]
62 The square on the operational curve for , = 1 (dotted line) indicates the equilibrium state corresponding to gt. [sent-201, score-0.281]
63 A rapid increase from g8 = gt to g8 = gt + gp (rightward solid arrow) is followed by an increase in Vm towards its equilibrium value (upward dotted arrow). [sent-202, score-0.491]
64 When the phasic input is removed (leftward solid arrow), Vm decreases to its initial equilibrium value (down- 9D-U 9; enhanced amplitude 9t N E c75 6 enhanced amplitude and 7. [sent-203, score-0.372]
65 5 d) No Response O-l-----~-~___>,~"t_, o Figure 3: Modulation of response in high dopamine relative to low dopamine conditions as a function of the strength of phasic and tonic inputs. [sent-204, score-1.224]
66 In unrewarded trials, the only difference between a larger and a smaller phasic input is that the former results in a more depolarized membrane potential and thus a higher firing rate. [sent-206, score-0.628]
67 The firing activity, which ceases when the phasic input disappears, encodes for the strength of the sensory-related stimulus. [sent-207, score-0.266]
68 The phasic input is the conditioned stimulus that triggers dopamine release in the striatum, and the operational curve switches from the '"Y = 1 (dotted) curve to the bistable '"Y = 1. [sent-209, score-1.011]
69 The consequences of this switch depend on the strength of the phasic input. [sent-211, score-0.178]
70 If g8 exceeds the value for the D-+ U transition (Fig 2A) , Vm depolarizes towards the upper branch of the bistable operational curve. [sent-212, score-0.384]
71 This additional depolarization results in a noticeably higher firing rate than the one elicited by the same input in an unrewarded trial (Fig 2A, left panel). [sent-213, score-0.253]
72 When the phasic input is removed, the unit hyperpolarizes slightly as it reaches the upper branch of the bistable operational curve. [sent-214, score-0.559]
73 If gt exceeds gU--+D, the unit remains in the up state until '"Y decreases towards its baseline level. [sent-215, score-0.195]
74 If this condition is met in a rewarded trial, the response is not only larger in amplitude but also longer in duration. [sent-216, score-0.158]
75 In contrast to these enhancements, if g8 is not sufficient to exceed g; (Fig 2B), Vm hyperpolarizes towards the lower branch of the bistable operational curve. [sent-217, score-0.425]
76 In this type of rewarded trial, dopamine suppresses the response of the unit. [sent-219, score-0.629]
77 The analysis presented above provides an explanatory mechanism for the observation of either enhanced or suppressed spiny neuron activity in the presence of dopamine. [sent-220, score-0.611]
78 It is the strength of the total synaptic input that selects between these two effects; the generic features of their differentiation are summarized in Fig 3. [sent-221, score-0.15]
79 4 Information processing Dopamine induced bistability improves the ability of the model spiny neuron to detect time correlated sensory-related inputs relative to a context-related background. [sent-226, score-0.55]
80 2 J-LS/cm 2 consists of two PDFs corresponding to gp = 0 (left; black line) and gp = 5. [sent-231, score-0.246]
81 These two values of gp occur with equal prior probability; time correlations are introduced through a repeat probability Pr of retaining the current value of gp in the subsequent time step. [sent-233, score-0.282]
82 c B A D o -60 Vm (mV) Vm (mV) -30 Vm (mV) Figure 4: Probability density functions for (A) synaptic input, (B) membrane potential at "( = 1, (C) membrane potential at "( = 1. [sent-237, score-0.455]
83 The transformation of g8 into Vm through the "( = 1 operational curve results in the PDFs shown in Fig 4B; here again, the total PDF does not depend on Pr. [sent-242, score-0.19]
84 4 operational curve, the PDFs that characterize Vm depend on Pr and are shown in Fig 4C (Pr = 0. [sent-246, score-0.149]
85 975, which describes phasic input persistance for about 400 ms). [sent-248, score-0.185]
86 A single separating boundary in the gap between the two stable branches is suboptimal, but is easily implement able by the bistable neuron. [sent-253, score-0.2]
87 4 clearly indicate that ambiguities in the bistable region make it harder to identify temporally uncorrelated instances of gp -::f- 0 on the basis of a single separating boundary (Fig 4C), while performance improves if instances with gp -::f- 0 are correlated over time (Fig 4D). [sent-259, score-0.405]
88 5 Conclusions The model presented here incorporates the most relevant effects of dopamine neuromodulation of striatal medium spiny neurons via D1 receptor activation. [sent-261, score-1.17]
89 In the absence of dopamine the model reproduces the bimodal character of medium spiny neurons [5]. [sent-262, score-0.99]
90 This qualitative change in character provides a mechanism to account for both enhancement and depression of spiny neuron discharge in response to inputs associated with expectation of reward. [sent-264, score-0.616]
91 There is only limited direct experimental evidence of bistability in the membrane potential of spiny neurons: the sustained depolarization observed in vitro following brief current injection in the presence of D1 agonists [4] is a hallmark of bistable responsiveness. [sent-265, score-0.85]
92 The activity of single striatal spiny neurons recorded in a memory guided saccade task [1] is strongly modulated by the expectation of reward as reinforcement for correct performance. [sent-266, score-0.691]
93 In these experiments, most units show a more intense response of longer duration to the presentation of visual stimuli indicative of upcoming reward; a few units show instead suppressed activity. [sent-267, score-0.148]
94 Bistability provides a gain mechanism that nonlinearly amplifies both the intensity and duration of striatal activity. [sent-270, score-0.158]
95 The model indicates that through the activation of D1 receptors, dopamine can temporarily desensitize spiny neurons to weak inputs while simultaneously sensitizing spiny neurons to large inputs. [sent-272, score-1.39]
96 A computational advantage of this mechanism is the potential adaptability of signal modulation: the brain may be able to utilize the demonstrated plasticity of corti costriatal synapses so that dopamine release preferentially enhances salient signals related to reward. [sent-273, score-0.581]
97 This selective enhancement of striatal activity would result in a more informative efferent signal related to achieving reward. [sent-274, score-0.206]
98 At the systems level, dopamine plays a significant role in the normal operation of the brain, as evident in the severe cognitive and motor deficits associated with pathologies ofthe dopamine system (e. [sent-275, score-0.942]
99 Yet at the cellular level, the effect of dopamine on the physiology of neurons seems modest. [sent-278, score-0.59]
100 Other models have suggested that dopamine modulates contrast [9], but the temporal effect is a novel aspect that plays an important role in information processing. [sent-280, score-0.55]
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Abstract: Identity uncertainty is a pervasive problem in real-world data analysis. It arises whenever objects are not labeled with unique identifiers or when those identifiers may not be perceived perfectly. In such cases, two observations may or may not correspond to the same object. In this paper, we consider the problem in the context of citation matching—the problem of deciding which citations correspond to the same publication. Our approach is based on the use of a relational probability model to define a generative model for the domain, including models of author and title corruption and a probabilistic citation grammar. Identity uncertainty is handled by extending standard models to incorporate probabilities over the possible mappings between terms in the language and objects in the domain. Inference is based on Markov chain Monte Carlo, augmented with specific methods for generating efficient proposals when the domain contains many objects. Results on several citation data sets show that the method outperforms current algorithms for citation matching. The declarative, relational nature of the model also means that our algorithm can determine object characteristics such as author names by combining multiple citations of multiple papers. 1 INTRODUCTION Citation matching is the problem currently handled by systems such as Citeseer [1]. 1 Such systems process a large number of scientific publications to extract their citation lists. By grouping together all co-referring citations (and, if possible, linking to the actual cited paper), the system constructs a database of “paper” entities linked by the “cites(p 1 , p2 )” relation. This is an example of the general problem of determining the existence of a set of objects, and their properties and relations, given a collection of “raw” perceptual data; this problem is faced by intelligence analysts and intelligent agents as well as by citation systems. A key aspect of this problem is determining when two observations describe the same object; only then can evidence be combined to develop a more complete description of the object. Objects seldom carry unique identifiers around with them, so identity uncertainty is ubiquitous. For example, Figure 1 shows two citations that probably refer to the same paper, despite many superficial differences. Citations appear in many formats and are rife with errors of all kinds. As a result, Citeseer—which is specifically designed to overcome such problems—currently lists more than 100 distinct AI textbooks published by Russell 1 See citeseer.nj.nec.com. Citeseer is now known as ResearchIndex. [Lashkari et al 94] Collaborative Interface Agents, Yezdi Lashkari, Max Metral, and Pattie Maes, Proceedings of the Twelfth National Conference on Articial Intelligence, MIT Press, Cambridge, MA, 1994. Metral M. Lashkari, Y. and P. Maes. Collaborative interface agents. In Conference of the American Association for Artificial Intelligence, Seattle, WA, August 1994. Figure 1: Two citations that probably refer to the same paper. and Norvig on or around 1995, from roughly 1000 citations. Identity uncertainty has been studied independently in several fields. Record linkage [2] is a method for matching up the records in two files, as might be required when merging two databases. For each pair of records, a comparison vector is computed that encodes the ways in which the records do and do not match up. EM is used to learn a naive-Bayes distribution over this vector for both matched and unmatched record pairs, so that the pairwise match probability can then be calculated using Bayes’ rule. Linkage decisions are typically made in a greedy fashion based on closest match and/or a probability threshold, so the overall process is order-dependent and may be inconsistent. The model does not provide for a principled way to combine matched records. A richer probability model is developed by Cohen et al [3], who model the database as a combination of some “original” records that are correct and some number of erroneous versions. They give an efficient greedy algorithm for finding a single locally optimal assignment of records into groups. Data association [4] is the problem of assigning new observations to existing trajectories when multiple objects are being tracked; it also arises in robot mapping when deciding if an observed landmark is the same as one previously mapped. While early data association systems used greedy methods similar to record linkage, recent systems have tried to find high-probability global solutions [5] or to approximate the true posterior over assignments [6]. The latter method has also been applied to the problem of stereo correspondence, in which a computer vision system must determine how to match up features observed in two or more cameras [7]. Data association systems usually have simple observation models (e.g., Gaussian noise) and assume that observations at each time step are all distinct. More general patterns of identity occur in natural language text, where the problem of anaphora resolution involves determining whether phrases (especially pronouns) co-refer; some recent work [8] has used an early form of relational probability model, although with a somewhat counterintuitive semantics. Citeseer is the best-known example of work on citation matching [1]. The system groups citations using a form of greedy agglomerative clustering based on a text similarity metric (see Section 6). McCallum et al [9] use a similar technique, but also develop clustering algorithms designed to work well with large numbers of small clusters (see Section 5). With the exception of [8], all of the preceding systems have used domain-specific algorithms and data structures; the probabilistic approaches are based on a fixed probability model. In previous work [10], we have suggested a declarative approach to identity uncertainty using a formal language—an extension of relational probability models [11]. Here, we describe the first substantial application of the approach. Section 2 explains how to specify a generative probability model of the domain. The key technical point (Section 3) is that the possible worlds include not only objects and relations but also mappings from terms in the language to objects in the domain, and the probability model must include a prior over such mappings. Once the extended model has been defined, Section 4 details the probability distributions used. A general-purpose inference method is applied to the model. We have found Markov chain Monte Carlo (MCMC) to be effective for this and other applications (see Section 5); here, we include a method for generating effective proposals based on ideas from [9]. The system also incorporates an EM algorithm for learning the local probability models, such as the model of how author names are abbreviated, reordered, and misspelt in citations. Section 6 evaluates the performance of four datasets originally used to test the Citeseer algorithms [1]. As well as providing significantly better performance, our system is able to reason simultaneously about papers, authors, titles, and publication types, and does a good job of extracting this information from the grouped citations. For example, an author’s name can be identified more accurately by combining information from multiple citations of several different papers. The errors made by our system point to some interesting unmodeled aspects of the citation process. 2 RPMs Reasoning about identity requires reasoning about objects, which requires at least some of the expressive power of a first-order logical language. Our approach builds on relational probability models (RPMs) [11], which let us specify probability models over possible worlds defined by objects, properties, classes, and relations. 2.1 Basic RPMs At its most basic, an RPM, as defined by Koller et al [12], consists of • A set C of classes denoting sets of objects, related by subclass/superclass relations. • A set I of named instances denoting objects, each an instance of one class. • A set A of complex attributes denoting functional relations. Each complex attribute A has a domain type Dom[A] ∈ C and a range type Range[A] ∈ C. • A set B of simple attributes denoting functions. Each simple attribute B has a domain type Dom[B] ∈ C and a range V al[B]. • A set of conditional probability models P (B|P a[B]) for the simple attributes. P a[B] is the set of B’s parents, each of which is a nonempty chain of (appropriately typed) attributes σ = A1 . · · · .An .B , where B is a simple attribute. Probability models may be attached to instances or inherited from classes. The parent links should be such that no cyclic dependencies are formed. • A set of instance statements, which set the value of a complex attribute to an instance of the appropriate class. We also use a slight variant of an additional concept from [11]: number uncertainty, which allows for multi-valued complex attributes of uncertain cardinality. We define each such attribute A as a relation rather than a function, and we associate with it a simple attribute #[A] (i.e., the number of values of A) with a domain type Dom[A] and a range {0, 1, . . . , max #[A]}. 2.2 RPMs for citations Figure 2 outlines an RPM for the example citations of Figure 1. There are four classes, the self-explanatory Author, Paper, and Citation, as well as AuthorAsCited, which represents not actual authors, but author names as they appear when cited. Each citation we wish to match leads to the creation of a Citation instance; instances of the remaining three classes are then added as needed to fill all the complex attributes. E.g., for the first citation of Figure 1, we would create a Citation instance C1 , set its text attribute to the string “Metral M. ...August 1994.”, and set its paper attribute to a newly created Paper instance, which we will call P1 . We would then introduce max(#[author]) (here only 3, for simplicity) AuthorAsCited instances (D11 , D12 , and D13 ) to fill the P1 .obsAuthors (i.e., observed authors) attribute, and an equal number of Author instances (A 11 , A12 , and A13 ) to fill both the P1 .authors[i] and the D1i .author attributes. (The complex attributes would be set using instance statements, which would then also constrain the cited authors to be equal to the authors of the actual paper. 2 ) Assuming (for now) that the value of C1 .parse 2 Thus, uncertainty over whether the authors are ordered correctly can be modeled using probabilistic instance statements. A11 Author A12 surname #(fnames) fnames A13 A21 D11 AuthorAsCited surname #(fnames) fnames author A22 A23 D12 D13 D21 D22 Paper D23 Citation #(authors) authors title publication type P1 P2 #(obsAuthors) obsAuthors obsTitle parse C1 C2 text paper Figure 2: An RPM for our Citeseer example. The large rectangles represent classes: the dark arrows indicate the ranges of their complex attributes, and the light arrows lay out all the probabilistic dependencies of their basic attributes. The small rectangles represent instances, linked to their classes with thick grey arrows. We omit the instance statements which set many of the complex attributes. is observed, we can set the values of all the basic attributes of the Citation and AuthorAsCited instances. (E.g., given the correct parse, D11 .surname would be set to Lashkari, and D12 .fnames would be set to (Max)). The remaining basic attributes — those of the Paper and Author instances — represent the “true” attributes of those objects, and their values are unobserved. The standard semantics of RPMs includes the unique names assumption, which precludes identity uncertainty. Under this assumption, any two papers are assumed to be different unless we know for a fact that they are the same. In other words, although there are many ways in which the terms of the language can map to the objects in a possible world, only one of these identity mappings is legal: the one with the fewest co-referring terms. It is then possible to express the RPM as an equivalent Bayesian network: each of the basic attributes of each of the objects becomes a node, with the appropriate parents and probability model. RPM inference usually involves the construction of such a network. The Bayesian network equivalent to our RPM is shown in Figure 3. 3 IDENTITY UNCERTAINTY In our application, any two citations may or may not refer to the same paper. Thus, for citations C1 and C2 , there is uncertainty as to whether the corresponding papers P 1 and P2 are in fact the same object. If they are the same, they will share one set of basic attributes; A11. surname D12. #(fnames) D12. surname A11. fnames D11. #(fnames) D12. fnames A21. #(fnames) A13. surname A12. fnames A21. fnames A13. fnames A13. #(fnames) D13. surname D11. fnames D11. surname D13. #(fnames) C1. #(authors) P1. title C1. text P1. pubtype C1. obsTitle A21. surname A23. surname A22. fnames D22. #(fnames) D12. surname D21. #(fnames) D22. fnames A23. fnames A23. #(fnames) D23. surname D21. fnames D13. fnames C1. parse A22. #(fnames) A22. surname A12. #(fnames) A12. surname A11. #(fnames) D23. fnames D21. surname D23. #(fnames) C2. #(authors) P2. title C2. parse C2. text C2. obsTitle P2. pubtype Figure 3: The Bayesian network equivalent to our RPM, assuming C 1 = C2 . if they are distinct, there will be two sets. Thus, the possible worlds of our probability model may differ in the number of random variables, and there will be no single equivalent Bayesian network. The approach we have taken to this problem [10] is to extend the representation of a possible world so that it includes not only the basic attributes of a set of objects, but also the number of objects n and an identity clustering ι, that is, a mapping from terms in the language (such as P1 ) to objects in the world. We are interested only in whether terms co-refer or not, so ι can be represented by a set of equivalence classes of terms. For example, if P1 and P2 are the only terms, and they co-refer, then ι is {{P1 , P2 }}; if they do not co-refer, then ι is {{P1 }, {P2 }}. We define a probability model for the space of extended possible worlds by specifying the prior P (n) and the conditional distribution P (ι|n). As in standard RPMs, we assume that the class of every instance is known. Hence, we can simplify these distributions further by factoring them by class, so that, e.g., P (ι) = C∈C P (ιC ). We then distinguish two cases: • For some classes (such as the citations themselves), the unique names assumptions remains appropriate. Thus, we define P (ιCitation ) to assign a probability of 1.0 to the one assignment where each citation object is unique. • For classes such as Paper and Author, whose elements are subject to identity uncertainty, we specify P (n) using a high-variance log-normal distribution. 3 Then we make appropriate uniformity assumptions to construct P (ιC ). Specifically, we assume that each paper is a priori equally likely to be cited, and that each author is a priori equally likely to write a paper. Here, “a priori” means prior to obtaining any information about the object in question, so the uniformity assumption is entirely reasonable. With these assumptions, the probability of an assignment ι C,k,m that maps k named instances to m distinct objects, when C contains n objects, is given by 1 n! P (ιC,k,m ) = (n − m)! nk When n > m, the world contains objects unreferenced by any of the terms. However, these filler objects are obviously irrelevant (if they affected the attributes of some named term, they would have been named as functions of that term.) Therefore, we never have to create them, or worry about their attribute values. Our model assumes that the cardinalities and identity clusterings of the classes are independent of each other, as well as of the attribute values. We could remove these assumptions. For one, it would be straightforward to specify a class-wise dependency model for n or ι using standard Bayesian network semantics, where the network nodes correspond to the cardinality attributes of the classes. E.g., it would be reasonable to let the total number of papers depend on the total number of authors. Similarly, we could allow ι to depend on the attribute values—e.g., the frequency of citations to a given paper might depend on the fame of the authors—provided we did not introduce cyclic dependencies. 4 The Probability Model We will now fill in the details of the conditional probability models. Our priors over the “true” attributes are constructed off-line, using the following resources: the 1990 Census data on US names, a large A.I. BibTeX bibliography, and a hand-parsed collection of 500 citations. We learn several bigram models (actually, linear combinations of a bigram model and a unigram model): letter-based models of first names, surnames, and title words, as well as higher-level models of various parts of the citation string. More specifically, the values of Author.fnames and Author.surname are modeled as having a a 0.9 chance of being 3 Other models are possible; for example, in situations where objects appear and disappear, P (ι) can be modeled implicitly by specifying the arrival, transition, and departure rates [6]. drawn from the relevant US census file, and a 0.1 chance of being generated using a bigram model learned from that file. The prior over Paper.titles is defined using a two-tier bigram model constructed using the bibliography, while the distributions over Author.#(fnames), Paper.#(authors), and Paper.pubType 4 are derived from our hand-parsed file. The conditional distributions of the “observed” variables given their true values (i.e., the corruption models of Citation.obsTitle, AuthorAsCited.surname, and AuthorAsCited.fnames) are modeled as noisy channels where each letter, or word, has a small probability of being deleted, or, alternatively, changed, and there is also a small probability of insertion. AuthorAsCited.fnames may also be abbreviated as an initial. The parameters of the corruption models are learnt online, using stochastic EM. Let us now return to Citation.parse, which cannot be an observed variable, since citation parsing, or even citation subfield extraction, is an unsolved problem. It is therefore fortunate that our approach lets us handle uncertainty over parses so naturally. The state space of Citation.parse has two different components. First of all, it keeps track of the citation style, defined as the ordering of the author and title subfields, as well as the format in which the author names are written. The prior over styles is learned using our hand-segmented file. Secondly, it keeps track of the segmentation of Citation.text, which is divided into an author segment, a title segment, and three filler segments (one before, one after, and one in between.) We assume a uniform distribution over segmentations. Citation.parse greatly constrains Citation.text: the title segment of Citation.text must match the value of Citation.obsTitle, while its author segment must match the combined values of the simple attributes of Citation.obsAuthors. The distributions over the remaining three segments of Citation.text are defined using bigram models, with the model used for the final segment chosen depending on the publication type. These models were, once more, learned using our pre-segmented file. 5 INFERENCE With the introduction of identity uncertainty, our model grows from a single Bayesian network to a collection of networks, one for each possible value of ι. This collection can be rather large, since the number of ways in which a set can be partitioned grows very quickly with the size of the set. 5 Exact inference is, therefore, impractical. We use an approximate method based on Markov chain Monte Carlo. 5.1 MARKOV CHAIN MONTE CARLO MCMC [13] is a well-known method for approximating an expectation over some distribution π(x), commonly used when the state space of x is too large to sum over. The weighted sum over the values of x is replaced by a sum over samples from π(x), which are generated using a Markov chain constructed to have π(x) as a stationary distribution. There are several ways of building up an appropriate Markov chain. In the Metropolis– Hastings method (M-H), transitions in the chain are constructed in two steps. First, a candidate next state x is generated from the current state x, using the (more or less arbitrary) proposal distribution q(x |x). The probability that the move to x is actually made is the acceptance probability, defined as α(x |x) = min 1, π(x )q(x|x ) . π(x)q(x |x) Such a Markov chain will have the right stationary distribution π(x) as long as q is defined in such a way that the chain is ergodic. It is even possible to factor q into separate proposals for various subsets of variables. In those situations, the variables that are not changed by the transition cancel in the ratio π(x )/π(x), so the required calculation can be quite simple. 4 Publication types range over {article, conference paper, book, thesis, and tech report} This sequence is described by the Bell numbers, whose asymptotic behaviour is more than exponential. 5 5.2 THE CITATION-MATCHING ALGORITHM The state space of our MCMC algorithm is the space of all the possible worlds, where each possible world contains an identity clustering ι, a set of class cardinalities n, and the values of all the basic attributes of all the objects. Since the ι is given in each world, the distribution over the attributes can be represented using a Bayesian network as described in Section 3. Therefore, the probability of a state is simply the product pf P (n), P (ι), and the probability of the hidden attributes of the network. Our algorithm uses a factored q function. One of our proposals attempts to change n using a simple random walk. The other suggests, first, a change to ι, and then, values for all the hidden attributes of all the objects (or clusters in ι) affected by that change. The algorithm for proposing a change in ιC works as follows: Select two clusters a1 , a2 ∈ ιC 6 Create two empty clusters b1 and b2 place each instance i ∈ a1 ∪ a2 u.a.r. into b1 or b2 Propose ιC = ιC − {a1, a2} ∪ {b1, b2} Given a proposed ιC , suggesting values for the hidden attributes boils down to recovering their true values from (possibly) corrupt observations, e.g., guessing the true surname of the author currently known both as “Simth” and “Smith”. Since our title and name noise models are symmetric, our basic strategy is to apply these noise models to one of the observed values. In the case of surnames, we have the additional resource of a dictionary of common names, so, some of the time, we instead pick one of the set of dictionary entries that are within a few corruptions of our observed names. (One must, of course, careful to account for this hybrid approach in our acceptance probability calculations.) Parses are handled differently: we preprocess each citation, organizing its plausible segmentations into a list ordered in terms of descending probability. At runtime, we simply sample from these discrete distributions. Since we assume that boundaries occur only at punctuation marks, and discard segmentations of probability < 10−6 , the lists are usually quite short. 7 The publication type variables, meanwhile, are not sampled at all. Since their range is so small, we sum them out. 5.3 SCALING UP One of the acknowledged flaws of the MCMC algorithm is that it often fails to scale. In this application, as the number of papers increases, the simplest approach — one where the two clusters a1 and a2 are picked u.a.r — is likely to lead to many rejected proposals, as most pairs of clusters will have little in common. The resulting Markov chain will mix slowly. Clearly, we would prefer to focus our proposals on those pairs of clusters which are actually likely to exchange their instances. We have implemented an approach based on the efficient clustering algorithm of McCallum et al [9], where a cheap distance metric is used to preprocess a large dataset and fragment it into many canopies, or smaller, overlapping sets of elements that have a non-zero probability of matching. We do the same, using word-matching as our metric, and setting the thresholds to 0.5 and 0.2. Then, at runtime, our q(x |x) function proposes first a canopy c, and then a pair of clusters u.a.r. from c. (q(x|x ) is calculated by summing over all the canopies which contain any of the elements of the two clusters.) 6 EXPERIMENTAL RESULTS We have applied the MCMC-based algorithm to the hand-matched datasets used in [1]. (Each of these datasets contains several hundred citations of machine learning papers, about half of them in clusters ranging in size from two to twenty-one citations.) We have also 6 7 Note that if the same cluster is picked twice, it will probably be split. It would also be possible to sample directly from a model such as a hierarchical HMM Face Reinforcement Reasoning Constraint 349 citations, 242 papers 406 citations, 148 papers 514 citations, 296 papers 295 citations, 199 papers Phrase matching 94% 79% 86% 89% RPM + MCMC 97% 94% 96% 93% Table 1: Results on four Citeseer data sets, for the text matching and MCMC algorithms. The metric used is the percentage of actual citation clusters recovered perfectly; for the MCMC-based algorithm, this is an average over all the MCMC-generated samples. implemented their phrase matching algorithm, a greedy agglomerative clustering method based on a metric that measures the degrees to which the words and phrases of any two citations overlap. (They obtain their “phrases” by segmenting each citation at all punctuation marks, and then taking all the bigrams of all the segments longer than two words.) The results of our comparison are displayed in Figure 1, in terms of the Citeseer error metric. Clearly, the algorithm we have developed easily beats our implementation of phrase matching. We have also applied our algorithm to a large set of citations referring to the textbook Artificial Intelligence: A Modern Approach. It clusters most of them correctly, but there are a couple of notable exceptions. Whenever several citations share the same set of unlikely errors, they are placed together in a separate cluster. This occurs because we do not currently model the fact that erroneous citations are often copied from reference list to reference list, which could be handled by extending the model to include a copiedFrom attribute. Another possible extension would be the addition of a topic attribute to both papers and authors: tracking the authors’ research topics might enable the system to distinguish between similarly-named authors working in different fields. Generally speaking, we expect that relational probabilistic languages with identity uncertainty will be a useful tool for creating knowledge from raw data. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] S. Lawrence, K. Bollacker, and C. Lee Giles. Autonomous citation matching. In Agents, 1999. I. Fellegi and A. Sunter. A theory for record linkage. In JASA, 1969. W. Cohen, H. Kautz, and D. McAllester. Hardening soft information sources. In KDD, 2000. Y. Bar-Shalom and T. E. Fortman. Tracking and Data Association. Academic Press, 1988. I. J. Cox and S. Hingorani. An efficient implementation and evaluation of Reid’s multiple hypothesis tracking algorithm for visual tracking. In IAPR-94, 1994. H. Pasula, S. Russell, M. Ostland, and Y. Ritov. Tracking many objects with many sensors. In IJCAI-99, 1999. F. Dellaert, S. Seitz, C. Thorpe, and S. Thrun. Feature correspondence: A markov chain monte carlo approach. In NIPS-00, 2000. E. Charniak and R. P. Goldman. A Bayesian model of plan recognition. AAAI, 1993. A. McCallum, K. Nigam, and L. H. Ungar. Efficient clustering of high-dimensional data sets with application to reference matching. In KDD-00, 2000. H. Pasula and S. Russell. Approximate inference for first-order probabilistic languages. In IJCAI-01, 2001. A. Pfeffer. Probabilistic Reasoning for Complex Systems. PhD thesis, Stanford, 2000. A. Pfeffer and D. Koller. Semantics and inference for recursive probability models. In AAAI/IAAI, 2000. W.R. Gilks, S. Richardson, and D.J. Spiegelhalter. Markov chain Monte Carlo in practice. Chapman and Hall, London, 1996.
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