Koller, D. and Fratkina, R. (1998). Using learning for approximation in stochastic processes, Proc. of the International Conference on Machine Learning (ICML).  Home/Search   Document Details and Download   Summary   Related Articles   Check

....more promising approach would be to develop variable resolution methods in which a coarse scale time model is piecewise refined until further splitting of time intervals does not cause significant changes in the predictive distributions. Such an approach is similar to tree based density estimation [113, 83, 101]. Variable timeresolution will also lend itself to an anytime implementation; instead of fixing a significance threshold, the system will continually refine the discretization so as to maximize accuracy given available computational resources. Finally, we also expect drastic improvements from the ....

D. Koller and R. Fratkina. Using learning for approximation in stochastic processes. In Proc. of the International Conference on Machine Learning, 1998.

....The VRPF generalizes from current samples to unsampled regions of the state space. Regions of the state space that had no samples at time t may acquire samples at time t 1 on abstraction. This provides additional robustness to noise that may have resulted in eliminating a likely hypothesis. [Koller and Fratkina, 1998] addresses this by using the time t samples as input to a density estimation algorithm that learns a distribution over the states at time t. Samples at time t 1 are then generated using this generalized distribution. Ng et al. 2002] uses a factored representation to allow a similar mixing of ....

D. Koller and R. Fratkina. Using learning for approximation in stochastic processes. In ICML, 1998.

.... The probability density function is one of the important factors in the defined knowledge gain in (3) In machine learning literature, there have been many efficient ways for density estimation, such as the Nave density estimator, the Bayesian networks, the mixture models, the density trees [28], and the kernel density estimator [27] also known as Parzen windows) We use the kernel density estimator. The kernel method is also used in updating the probability lists in the next subsection. Since the probability density estimation is independent of the latter probability list updating and ....

D. Koller and R. Fratkina, "Using learning for approximation in stochastic processes," in Proc. ICML'98.

....[2] most existing approaches to particle filters use a fixed number of samples during the whole state estimation process. This can be highly inefficient, since the complexity of the probability densities can vary drastically over time. An adaptive approach for particle filters has been applied by [8] and [5] This approach adjusts the number of samples based on the likelihood of observations, which has some important shortcomings, as we will show. In this paper we introduce a novel approach to adapting the number of samples over time. Our technique determines the number of samples based on ....

....3.1 Likelihood based adaptation We call this approach likelihood based adaptation since it determines the number of samples such that the sum of non normalized likelihoods (importance weights) exceeds a prespecified threshold. This approach has been applied to dynamic Bayesian networks [8] and mobile robot localization [5] The intuition behind this approach can be illustrated in the robot localization context: If the sample set is well in tune with the sensor reading, each individual importance weight is large and the sample set remains small. This is typically the case during ....

[Article contains additional citation context not shown here]

D. Koller and R. Fratkina. Using learning for approximation in stochastic processes. In Proc. of the International Conference on Machine Learning (ICML), 1998.

....that are in widespread use of robotics and engineering. They are also at the core of virtually any successful CML SLAM algorithm [85] Special versions of Bayes lters are known as Kalman lters [41] hidden Markov models [68, 67] particle lters [22, 23, 52, 66] and dynamic belief networks [16, 44, 73]. The classical probabilistic occupancy grid mapping algorithm [25, 59] is also a (binary) Bayes lter. Bayes lters address the problem of estimating the state of a time varying (dynamic) system such as a mobile robot from sensor measurements. Let us denote the state of the environment by x; the ....

D. Koller and R. Fratkina. Using learning for approximation in stochastic processes. In Proceedings of the International Conference on Machine Learning (ICML), 1998.

....are at the core of the algorithm presented here. They comprise a popular class of Bayesian estimation algorithms that are in widespread use of robotics and engineering. Special versions of Bayes filters are known as Kalman filters [28] hidden Markov models [53, 52] and dynamic belief networks [9, 31, 56]. The classical probabilistic occupancy grid mapping algorithm [15, 44] is also a (binary) Bayes filter. Bayes filtering addresses the problem of estimating an unknown quantity from sensor measurements. In its most general form, it can estimate the state of a timevarying (dynamic) system, such as ....

D. Koller and R. Fratkina. Using learning for approximation in stochastic processes. In Proceedings of the International Conference on Machine Learning (ICML), 1998.

....4 Delta 10 numbers are needed to specify an arbitrary probability distribution over all floating point values at 4 byte resolution. The statistical literature offers many compact representations, such as mixtures of Gaussians [22] piecewise constant functions [13] Monte Carlo approximations [44, 50], trees [8, 71] and other variable resolution methods [77] In our current implementation all probability distributions are represented by piecewise constant density functions. The granularity of this function can be determined by the programmer, by setting the system level variable prob dist ....

....regions with high likelihood) would be advantageous. The use of piecewise constant representations is not a limitation of the language per se; it is only a shortcoming of our current implementation. Several other options exist, such as such as mixtures of Gaussians [22] Monte Carlo approximations [21, 44, 50], and variable resolution methods such as trees [8, 71, 77] Of particular interest are resource adaptive algorithms which can adapt their resource consumptions in accordance with the available resources [19] Probabilistic representations facilitate the design of resource adaptive mechanisms by ....

D. Koller and R. Fratkina. Using learning for approximation in stochastic processes. In Proceedings of the International Conference on Machine Learning (ICML), 1998.

....samples over time. Most existing approaches use a fixed number of samples during the whole state estimation process. However, this can be highly inefficient, since the complexity of the probability densities can vary drastically over time. An exception is the adaptive sampling approach applied by [14] and [7] Both approaches adjust the number of samples based on the likelihood of observations. Unfortunately, this method has some important shortcomings, as we will show. In this paper we introduce a novel approach to adapting the number of samples over time. In contrast to previous approaches, ....

....adaptation We call this approach likelihood based adaptation since it is based on the idea of determining the number of samples such that the non normalized sum of likelihoods (importance weights) exceeds a pre specified threshold. This approach has been applied to dynamic Bayesian networks [14] and mobile robot localization [7] The intuition behind this approach can be illustrated in the robot localization context: If the sample set is well in tune with the sensor reading, each individual 5 importance weight is large and the sample set remains small. This is typically the case during ....

[Article contains additional citation context not shown here]

D. Koller and R. Fratkina. Using learning for approximation in stochastic processes. In Proc. of the International Conference on Machine Learning (ICML), 1998.

....of resampling algorithms in tracking. The best known algorithm is known as CONDENSATION in the vision community [2] and survival of the fittest in the AI community [15] A natural variant on this algorithm is to represent the intermediate stages by an approximation derived from the samples (e.g. [16]) 2 Maximum likelihood methods for structure from motion Accurate solutions to structure from motion are attractive, because the technique can be used to generate models for rendering virtual environments (e.g. 5, 24] Assume distinct views of points are given. In the influential ....

D. Koller and R. Fratkina. Using learning for approximation in stochastic processes. In Proc. Machine Learning, 1998.

....the uncertainty of both robots during localization. To accommodate the noise and ambiguity arising in real world domains, detection models are probabilistic, capturing the reliability and accuracy of robot detection. The constraint propagation is implemented using sampling, and density trees [38, 49, 52, 53] are employed to integrate information from other robots into a robot s belief. While our approach is applicable to any sensor capable of (occasionally) detecting other robots, we present an implementation that uses color cameras and laser range finders for robot detection. The parameters of the ....

.... samples, however, MCL can effectively re localize the robot, as documented in our experiments described in [21] see also the discussion on loss of diversity in [18] Another modification to the basic approach is based on the observation that the best sample set sizes can vary drastically [38]. During global localization, a robot may be completely ignorant as to where it is; hence, it s belief uniformly covers its full three dimensional state space. During position tracking, on the other hand, the uncertainty is typically small. MCL determines the sample set size on the fly: It ....

[Article contains additional citation context not shown here]

D. Koller and R. Fratkina. Using learning for approximation in stochastic processes. In Proc. of the International Conference on Machine Learning (ICML), 1998.

....the danger of generating pairs of poses hx (i) t ; x (i) t Gamma1 i for which w (i) 0, but it involves an explicit forward sampling phase. The kd tree effectively smoothes the resulting density, which further reduces the variance of the estimation at the expense of introducing bias [35,33]. However, the primary role 22 Algorithm dual MCL 3(X; a; o) X 0 = for i = 0 to m do generate random x p(xjo) o) generate random x 0 p(xja; x 0 ) xja) w = Bel(x 0 ) add hx; wi to X 0 endfor normalize the importance factors w in X 0 return X 0 Table 2 The dual MCL ....

D. Koller and R. Fratkina. Using learning for approximation in stochastic processes. In Proceedings of the International Conference on Machine Learning (ICML), 1998.

....requires the multiplication of two densities which means that we have to establish a correspondence between the individual samples in Bel(Lm ) and the density representing the robot detection. To remedy this problem, our approach transforms sample sets into density functions using density trees [17, 22]. These methods approximate sample sets using piecewise constant density functions represented by a tree. The resolution of the tree is a function of the densities of the samples: the more samples exist in a region of space, the more fine grained the tree representation. Figure 1 shows an example ....

D. Koller and R. Fratkina. Using learning for approximation in stochastic processes. In Proc. of the International Conference on Machine Learning (ICML), 1998.

....the uncertainty of both robots during localization. To accommodate the noise and ambiguity arising in real world domains, detection models are probabilistic, capturing the reliability and accuracy of robot detection. The constraint propagation is implemented using sampling, and density trees [38, 49, 52, 53] are employed to integrate information from other robots into a robot s belief. While our approach is applicable to any sensor capable of (occasionally) detecting other robots, we present an implementation that uses color cameras and laser range finders for robot detection. The parameters of the ....

.... samples, however, MCL can effectively re localize the robot, as documented in our experiments described in [21] see also the discussion on loss of diversity in [18] Another modification to the basic approach is based on the observation that the best sample set sizes can vary drastically [38]. During global localization, a robot may be completely ignorant as to where it is; hence, it s belief uniformly covers its full three dimensional state space. During position tracking, on the other hand, the uncertainty is typically small. MCL determines the sample set size on the fly: It ....

[Article contains additional citation context not shown here]

D. Koller and R. Fratkina. Using learning for approximation in stochastic processes. In Proc. of the International Conference on Machine Learning (ICML), 1998.

....problem. Our approach basically ignores these non trivial interdependencies and instead represents the belief at time t by the product of its marginals Bel(x t ) N Y i=1 Bel(x i t ) 4. 1) Thus, our representation effectively makes a (false) independence assumption see (Boyen and Koller 1998) for an idea how to overcome this independence assumption while still avoiding the exponential death of the full product space. When a robot detects another robot, the observation is folded into a robot s current belief, and the result is used to update the belief of the other robots. More ....

....robot i s belief about the position of robot j. However, both of these densities are themselves represented by sample sets, and with probability one no two samples in these sets are the same. To solve this problem, our approach transforms sample sets into density functions using density trees (Koller and Fratkina 1998, Moore et al. 1997, Omohundro 1991) Density trees are continuations of sample sets which approximate the underlying density using a variable resolution piecewise constant density. Figure 16 shows such a tree, which corresponds to a robot s estimate of another robot s location. Together with ....

Koller, D. and Fratkina, R. (1998). Using learning for approximation in stochastic processes, Proc. of the International Conference on Machine Learning (ICML).

....loss in decision quality. We also suggest a heuristic method for choosing good projection schemes given the value function associated with a POMDP. Finally, we discuss how our techniques can also be applied to approximation methods other than projection (e.g. aggregation using density trees [13]) 2 POMDPs and Belief State Monitoring 2.1 Solving POMDPs A partially observable Markov decision process (POMDP) is a general model for decision making under uncertainty. Formally, we require the following components: a finite state space S; a finite action space A; a finite observation space ....

....our analysis is better suited to linear approximations: the constraints on the approximate belief state S(b) if linear, allow us to construct exact switch sets Sw(ff) rather than approximations, providing still tighter bounds. One linear approximation scheme involves the use of density trees [13]. A density tree represents a distribution by aggregation: the tree splits on variables, and probabilities labeling the leaves denote the probabilityof every state consistent with the corresponding branch. For instance, the tree in Figure 7 denotes a distribution over four variables in which ....

[Article contains additional citation context not shown here]

Daphne Koller and Raya Fratkina. Using learning for approximation in stochastic processes. In Proceedings of the 15th International Conference on Machine Learning, pages 287--295, Madison, 1998.

.... usually just consists of the robot s position and orientation (see Figure 1(a) If the state variables are discrete valued, we can perform Bayesian updating using a Hidden Markov Model (HMM) otherwise we can use (extended) Kalman filtering, or non parametric sample based filtering (see e.g. [KF98, TLF99]) For example, let us consider a simple HMM model in which the state consists of the robot s location X, which is represented as a point on a discrete grid, and the actions consist of moving one step in each of the four compass directions. The observation model specifies the probability of each ....

....at each end) and this can lead to less uncertainty about which part of the map to update. However, the (standard) assumption of parameter independence means this approach cannot handle correlations. Some alternative approximations would be to use sample based filtering algorithms (see e.g. [KF98, TLF99]) or the variational approximation of [GJ97] 3.1 Exact inference within a slice We will now discuss how to do inference in the two dimensional graphical model in Figure 2. Given the assumption that the M i;j s are independent, we only need to compute the marginals on each M i;j separately, ....

D. Koller and R. Fratkina. Using learning for approximation in stochastic processes. In Intl. Conf. on Machine Learning, 1998.

.... Pr(bja) xprior holds Pr(a) and yprior holds Pr(b) To perform direct manipulations using our sample based approximation of probability densities (e.g. for the data type prob double , an approximation of the (complete) density is temporarily constructed from the samples using density trees [11, 17]. Following the idea of importance factors [ two densities are combined by manipulating the sample probabilities of one sample set using the tree generated by the other sample set. Unfortunately, space limits prevent us from describing this mechanism in greater detail. 3 Learning To support ....

D. Koller and R. Fratkina. Using learning for approximation in stochastic processes. ICML-98.

....important in the local sampling approach. Here we also use our representation of the Q value distribution to propagate samples for other Q value distributions. Experience from monitoring tasks in stochastic processes suggest that introducing generalization can drastically improve performance (Koller Fratkina 1998). Perhaps the simplest approach to generalize from the k samples is to assume that the Q value distribution has a particular parametric form, and then to fit the parameters to the samples. The first approach that comes to mind is fitting a Gaussian to the k samples. This captures the first two ....

Koller, D. & Fratkina, R. (1998), Using learning for approximation in stochastic processes, in `Proceedings of the Fifteenth International Conference on Machine Learning', Morgan Kaufmann, San Francisco, Calif.

....the uncertainty of both robots during localization. To accommodate the noise and ambiguity arising in real world domains, detection models are probabilistic, capturing the reliability and accuracy of robot detection. The constraint propagation is implemented using sampling, and density trees [42, 51, 54, 55] are employed to integrate information from other robots into a robot s belief. While our approach is applicable to any sensor capable of (occasionally) detecting other robots, we present an implementation that uses color cameras for robot detection. Color images are continuously filtered, ....

....) and Bel( n ) are drawn randomly, it is not straightforward to establish correspondence between individual samples in Bel( m ) and R P ( t) m j (t) n ; r (t) n ) Bel( n ) d n . To remedy this problem, our approach transforms sample sets into density functions using density trees [42, 51, 54, 55]. These methods approximate sample sets using piecewise constant density functions represented by a tree. The resolution of the tree is a function of the densities of the samples: the more samples exist in a region of space, the finer grained the tree representation. Figure 4 shows an example ....

[Article contains additional citation context not shown here]

D. Koller and R. Fratkina. Using learning for approximation in stochastic processes. In Proceedings of the International Conference on Machine Learning (ICML), 1998.

....identical, and thus it is not straightforward how to obtain an approximation of their product f Delta g from X and Y . Notice that multiplications of densities are required by the Baum Welch algorithm (see e.g. Equation (13) Density trees, which are quite common in the statistical literature [24, 35, 38, 39], transform sample sets into density functions. Unfortunately, not all tree growing methods are asymptotically consistent when applied to samples generated from a density f . We will describe a simple algorithm which we will prove to be asymptotically consistent. Our algorithm annotates each node ....

....such sample sets is several orders of magnitude faster than the hand motion involved in gesture generation. This makes MCHMMs extremely fast for on line tracking and discrimination in this domain. Following suggestions by Koller 2 , we evaluated the utility of smoothing in the context of MCHMMs [13, 24]. Smoothing transforms those sample sets that represent posteriors over states (ff and fi) into more compact representations such as density trees, which are then used for likelihood weighted sampling instead of the original samples. To apply smoothing to MCHMMs, 2 personal communication 26 ....

[Article contains additional citation context not shown here]

D. Koller and R. Fratkina. Using learning for approximation in stochastic processes. In Proceedings of the International Conference on Machine Learning (ICML), 1998. Monte Carlo Hidden Markov Models 31

....represented by its own sample set. Unfortunately, with probability one, none of the samples in ff t and fi t are identical, and thus it is not straightforward how to obtain an approximation of their product. MCHMMs solve this problem by transforming sample sets into (non parametric) density trees [15, 22, 25], which effectively generalize discrete distributions (samples) to continuous distributions. Each node in a density tree is annotated with a hyper rectangular subspace of dom(f) denoted V (or V i for the i th node) Initially, all samples are assigned to the root node, which covers the entire ....

D. Koller and R. Fratkina. Using learning for approximation in stochastic processes. ICML-98.

....of resampling algorithms in tracking. The best known algorithm is known as CONDENSATION in the vision community [2] and survival of the fittest in the AI community [15] A natural variant on this algorithm is to represent the intermediate stages by an approximation derived from the samples (e.g. [16]) 2 Maximum likelihood methods for structure from motion Accurate solutions to structure from motion are attractive, because the technique can be used to generate models for rendering virtual environments (e.g. 5, 24] Assume m distinct views of n points are given. In the influential ....

D. Koller and R. Fratkina. Using learning for approximation in stochastic processes. In Proc. Machine Learning, 1998.

....4 Delta 10 9 numbers are needed to specify an arbitrary probability distribution over all floating point values at 4 byte resolution. The statistical literature offers many compact representations, such as mixtures of Gaussians [22] piecewise constant functions [13] Monte Carlo approximations [44, 50], trees [8, 71] and other variable resolution methods [77] In our current implementation all probability distributions are represented by piecewise constant density functions. The granularity of this function can be determined by the programmer, by setting the system level variable prob dist ....

....regions with high likelihood) would be advantageous. The use of piecewise constant representations is not a limitation of the language per se; it is only a shortcoming of our current implementation. Several other options exist, such as such as mixtures of Gaussians [22] Monte Carlo approximations [21, 44, 50], and variable resolution methods such as trees [8, 71, 77] Of particular interest are resource adaptive algorithms which can adapt their resource consumptions in accordance with the available resources [19] Probabilistic representations facilitate the design of resource adaptive mechanisms by ....

D. Koller and R. Fratkina. Using learning for approximation in stochastic processes. In Proceedings of the International Conference on Machine Learning (ICML), 1998. A Framework for Programming Embedded Systems: Initial Design and Results 43

....be applied in dynamic probabilistic networks (Kanazawa, Koller, Rus sell 1995) MCL uses fast sampling techniques to represent the robot s belief. When the robot moves or senses, importance re sampling (Rubin 1988) is applied to estimate the posterior distribution. An adaptive sampling scheme (Koller Fratkina 1998), which determines the number of samples on the fly, is employed to trade off computation and accuracy. As a result, MCL uses many samples during global localization when they are most needed, whereas the sample set size is small during tracking, when the position of the robot is approximately ....

....the other hand, the uncertainty is typically small and often focused on lowerdimensional manifolds. Thus, many more samples are needed during global localization to accurately approximate the true density, than are needed for position tracking. MCL determines the sample set size on the fly. As in (Koller Fratkina 1998), the idea is to use the divergence of P (l) and P (l j s) the belief before and after sensing, to determine the sample sets. More specifically, both motion data and sensor data is incorporated in a single step, and sampling is stopped whenever the sum of weights p (before normalization ) exceeds ....

Koller, D., and Fratkina, R. 1998. Using learning for approximation in stochastic processes. Proc. of ICML-98.

..... Generally speaking, this is just a hidden Markov model (HMM) How m m m m m m m m x 1 x 2 x 3 z 1 z 2 z 3 x T z T Figure 9: Generic diagram of a Markov model ever, many researchers have considered refinements to this model that incorporate structure in the state descriptions [ZR98, KKR95, KF98, IB98, BJ98, GJ97, Gha98]. The standard inference problem is to determine the posterior distribution over hidden state sequences hx 1 ; x T i, given the vector of observations hz 1 ; z T i. That is, we wish to make inferences about the target distribution P (x) PDN (xjz) Unfortunately, this posterior ....

D. Koller and R. Fratkina. Using learning for approximation in stochastic processes. In ICML, 1998.

....we estimate the probability density over the states of the system induced by at different points in time. These time slice densities completely determine the value of the policy . While density estimation is not an easy problem, we can utilize existing approaches to density propagation [3, 5], which allow users to specify prior knowledge about the densities, and which have also been shown, both theoretically and empirically, to provide robust estimates for time slice densities. We show how direct policy search can be implemented using this approach in two very different settings of ....

....(1) and then use them to compute the value. Unfortunately, that modification, by itself, does not resolve the difficulty. Representing and computing probability densities over large or infinite spaces is often no easier than representing and computing value functions. However, several results [3, 5] indicate that representing and computing high quality approximate densities may often be quite feasible. The general approach is an approximate density propagation algorithm, using time slice distributions in some restricted family . For example, in continuous spaces, might be the set of ....

[Article contains additional citation context not shown here]

D. Koller and R. Fratkina. Using learning for approximation in stochastic processes. In Proc. ICML, pages 287--295, 1998.

....In our case we needed a representation that enables us to express hybrid density functions. Furthermore, we were looking for a representation from which samples can be generated easily, and which can, in turn, be easily estimated from a set of samples. We chose to focus on Density Trees [13]. The structure of a density tree resembles that of a classification decision tree; however, rather than representing the conditional distribution of a class variable given a set of features, a density tree simply represents an unconditional density function over its set of random variables X. A ....

....and exhaustive events E u 1 ; E u k . Each branch from u corresponds to one of the events. The definition allows for arbitrary events; for example, we may have an interior node with three branches, corresponding to X 2 3, 3 X 2 5 and X 2 5. This definition generalizes that of [13]. The edge corresponding to the outcome E u i is labeled with the conditional probability of E u i given all the events on the path from the root to node u. We define the probability of a path as the product of all the probabilities along the path, i.e. the probability of the conjunction of the ....

[Article contains additional citation context not shown here]

D. Koller and R. Fratkina. Using learning for approximation in stochastic processes. In Proc. ICML, 1998.

....to operate on it effectively. Thus, rather than using an exact belief state which is very complex, we use a compactly represented approximate belief state. For example, in the context of a DBN, we might choose to represent an approximate belief state using a factored representation. See [12] for some discussion of possible belief state representations for DBNs. In the context of a hybrid process, we might choose to restrict the number of components in our Gaussian mixture. This idea immediately suggests a new scheme for monitoring a stochastic process: We first decide on some ....

....a simple approach of using domain knowledge to simply eliminate some of the variables from each time slice. The random sampling approach of [10] can also be viewed as maintaining an approximate belief state, albeit one represented very naively as a set of weighted samples. The recent work of [12] extends this idea, using the random samples at each time slice as data in order to learn an approximate belief state. Both of these ideas can be viewed as falling into the framework described in this paper. However, neither contains any analysis nor an explicit connection to the structure of the ....

[Article contains additional citation context not shown here]

D. Koller and R. Fratkina. Using learning for approximation in stochastic processes. In Proc. ML, 1998.

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Koller, D. and Fratkina, R. (1998). Using learning for approximation in stochastic processes, Proc. of the International Conference on Machine Learning (ICML).

No context found.

Daphne Koller and Raya Fratkina. Using learning for approximation in stochastic processes. In Proceedings of the 15th International Conference on Machine Learning, pages 287--295, Madison, 1998.

No context found.

Daphne Koller and Raya Fratkina. Using learning for approximation in stochastic processes. In Proceedings of the 15th International Conference on Machine Learning, pages 287-295, Madison, 1998.

No context found.

Koller, D. & Fratkina, R. (1998), Using learning for approximation in stochastic processes, in `Proceedings of the Fifteenth International Conference on Machine Learning', Morgan Kaufmann, San Francisco, Calif.

No context found.

D. Koller and R. Fratkina. Using learning for approximation in stochastic processes. In Proc. of the International Conference on Machine Learning, 1998.

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D. Koller and R. Fratkina, "Using learning for approximation in stochastic processes", ICML-98.

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D. Koller and R. Fratkina, "Using learning for approximation in stochastic processes", ICML-98. 35

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D. Koller and R. Fratkina. Using learning for approximation in stochastic processes. In Proc. of the International Conference on Machine Learning (ICML), 1998.

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