Our setting is a Partially Observable Markov Decision Process with continuous state, observation and action spaces. Decisions are based on a Particle Filter for estimating the belief state given past observations. We consider a policy gradient approach for parameterized policy optimization. For that purpose, we investigate sensitivity analysis of the performance measure with respect to the parameters of the policy, focusing on Finite Difference (FD) techniques. We show that the naive FD is subject to variance explosion because of the non-smoothness of the resampling procedure. We propose a more sophisticated FD method which overcomes this problem and establish its consistency.

We present a new framework for semi-supervised learning with sparse eigenfunction bases of kernel matrices. It turns out that when the \emph{cluster assumption} holds, that is, when the high density regions are sufficiently separated by low density valleys, each high density area corresponds to a unique representative eigenvector. Linear combination of such eigenvectors (or, more precisely, of their Nystrom extensions) provide good candidates for good classification functions. By first choosing an appropriate basis of these eigenvectors from unlabeled data and then using labeled data with Lasso to select a classifier in the span of these eigenvectors, we obtain a classifier, which has a very sparse representation in this basis. Importantly, the sparsity appears naturally from the cluster assumption. Experimental results on a number of real-world data-sets show that our method is competitive with the state of the art semi-supervised learning algorithms and outperforms the natural base-line algorithm (Lasso in the Kernel PCA basis).

We formulate and study a new variant of the $k$-armed bandit problem, motivated by e-commerce applications. In our model, arms have (stochastic) lifetime after which they expire. In this setting an algorithm needs to continuously explore new arms, in contrast to the standard $k$-armed bandit model in which arms are available indefinitely and exploration is reduced once an optimal arm is identified with near-certainty. The main motivation for our setting is online-advertising, where ads have limited lifetime due to, for example, the nature of their content and their campaign budget. An algorithm needs to choose among a large collection of ads, more than can be fully explored within the ads' lifetime. We present an optimal algorithm for the state-aware (deterministic reward function) case, and build on this technique to obtain an algorithm for the state-oblivious (stochastic reward function) case. Empirical studies on various reward distributions, including one derived from a real-world ad serving application, show that the proposed algorithms significantly outperform the standard multi-armed bandit approaches applied to these settings.

The learning of appropriate distance metrics is a critical problem in classification. In this work, we propose a boosting-based technique, termed BoostMetric, for learning a Mahalanobis distance metric. One of the primary difficulties in learning such a metric is to ensure that the Mahalanobis matrix remains positive semidefinite. Semidefinite programming is sometimes used to enforce this constraint, but does not scale well. BoostMetric is instead based on a key observation that any positive semidefinite matrix can be decomposed into a linear positive combination of trace-one rank-one matrices. BoostMetric thus uses rank-one positive semidefinite matrices as weak learners within an efficient and scalable boosting-based learning process. The resulting method is easy to implement, does not require tuning, and can accommodate various types of constraints. Experiments on various datasets show that the proposed algorithm compares favorably to those state-of-the-art methods in terms of classification accuracy and running time.

In this paper, we develop an efficient moments-based permutation test approach to improve the test--s computational efficiency by approximating the permutation distribution of the test statistic with Pearson distribution series. This approach involves the calculation of the first four moments of the permutation distribution. We propose a novel recursive method to derive these moments theoretically and analytically without any permutation. Experimental results using different test statistics are demonstrated using simulated data and real data. The proposed strategy takes advantage of nonparametric permutation tests and parametric Pearson distribution approximation to achieve both accuracy and efficiency.

Young children demonstrate the ability to make inferences about the preferences of other agents based on their choices. However, there exists no overarching account of what children are doing when they learn about preferences or how they use that knowledge. We use a rational model of preference learning, drawing on ideas from economics and computer science, to explain the behavior of children in several recent experiments. Specifically, we show how a simple econometric model can be extended to capture two- to four-year-olds’ use of statistical information in inferring preferences, and their generalization of these preferences.

Existing approaches to nonrigid structure from motion assume that the instantaneous 3D shape of a deforming object is a linear combination of basis shapes, which have to be estimated anew for each video sequence. In contrast, we propose that the evolving 3D structure be described by a linear combination of basis trajectories. The principal advantage of this lateral approach is that we do not need to estimate any basis vectors during computation. Instead, we show that generic bases over trajectories, such as the Discrete Cosine Transform (DCT) bases, can be used to effectively describe most real motions. This results in a significant reduction in unknowns, and corresponding stability, in estimation. We report empirical performance, quantitatively using motion capture data and qualitatively on several video sequences exhibiting nonrigid motions including piece-wise rigid motion, articulated motion, partially nonrigid motion (such as a facial expression), and highly nonrigid motion (such as a person dancing).

We develop new techniques for time series classification based on hierarchical Bayesian generative models (called mixed-effect models) and the Fisher kernel derived from them. A key advantage of the new formulation is that one can compute the Fisher information matrix despite varying sequence lengths and varying sampling intervals. This avoids the commonly-used ad hoc replacement of the Fisher information matrix with the identity which destroys the geometric invariance of the kernel. Our construction retains the geometric invariance, resulting in a kernel that is properly invariant under change of coordinates in the model parameter space. Experiments on detecting cognitive decline show that classifiers based on the proposed kernel outperform those based on generative models and other feature extraction routines, and on Fisher kernels that use the identity in place of the Fisher information.

We introduce a new type of Deep Belief Net and evaluate it on a 3D object recognition task. The top-level model is a third-order Boltzmann machine, trained using a hybrid algorithm that combines both generative and discriminative gradients. Performance is evaluated on the NORB database(normalized-uniform version), which contains stereo-pair images of objects under different lighting conditions and viewpoints. Our model achieves 6.5% error on the test set, which is close to the best published result for NORB (5.9%) using a convolutional neural net that has built-in knowledge of translation invariance. It substantially outperforms shallow models such as SVMs (11.6%). DBNs are especially suited for semi-supervised learning, and to demonstrate this we consider a modified version of the NORB recognition task in which additional unlabeled images are created by applying small translations to the images in the database. With the extra unlabeled data (and the same amount of labeled data as before), our model achieves 5.2% error, making it the current best result for NORB.

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