In this paper, we review the problem of matrix completion and expose its intimate relations with algebraic geometry, combinatorics and graph theory. We present the first necessary and sufficient combinatorial conditions for matrices of arbitrary rank to be identifiable from a set of matrix entries, yielding theoretical constraints and new algorithms for the problem of matrix completion. We conclude by algorithmically evaluating the tightness of the given conditions and algorithms for practically relevant matrix sizes, showing that the algebraic-combinatoric approach can lead to improvements over state-of-the-art matrix completion methods.

We study the task of online boosting--combining online weak learners into an online strong learner. While batch boosting has a sound theoretical foundation, online boosting deserves more study from the theoretical perspective. In this paper, we carefully compare the differences between online and batch boosting, and propose a novel and reasonable assumption for the online weak learner. Based on the assumption, we design an online boosting algorithm with a strong theoretical guarantee by adapting from the offline SmoothBoost algorithm that matches the assumption closely. We further tackle the task of deciding the number of weak learners using established theoretical results for online convex programming and predicting with expert advice. Experiments on real-world data sets demonstrate that the proposed algorithm compares favorably with existing online boosting algorithms.

We propose a novel interpretation of the collapsed variational Bayes inference with a zero-order Taylor expansion approximation, called CVB0 inference, for latent Dirichlet allocation (LDA). We clarify the properties of the CVB0 inference by using the alpha-divergence. We show that the CVB0 inference is composed of two different divergence projections: alpha=1 and -1. This interpretation will help shed light on CVB0 works.

In this paper, we present a simple non-parametric method for learning the structure of undirected graphs from data that drawn from an underlying unknown distribution. We propose to use Brownian distance covariance to estimate the conditional independences between the random variables and encodes pairwise Markov graph. This framework can be applied in high-dimensional setting, where the number of parameters much be larger than the sample size.

This paper proposes new formulas for the probabilities of causation difined by Pearl (2000). Tian and Pearl (2000a, 2000b) showed how to bound the quantities of the probabilities of causation from experimental and observational data, under the minimal assumptions about the data-generating process. We derive narrower bounds than Tian-Pearl bounds by making use of the covariate information measured in experimental and observational studies. In addition, we provide identifiable case under no-prevention assumption and discuss the covariate selection problem from the viewpoint of estimation accuracy. These results are helpful in providing more evidence for public policy assessment and dicision making problems.

SDYNA is a general framework designed to address large stochastic reinforcement learning problems. Unlike previous model based methods in FMDPs, it incrementally learns the structure and the parameters of a RL problem using supervised learning techniques. Then, it integrates decision-theoric planning algorithms based on FMDPs to compute its policy. SPITI is an instanciation of SDYNA that exploits ITI, an incremental decision tree algorithm, to learn the reward function and the Dynamic Bayesian Networks with local structures representing the transition function of the problem. These representations are used by an incremental version of the Structured Value Iteration algorithm. In order to learn the structure, SPITI uses Chi-Square tests to detect the independence between two probability distributions. Thus, we study the relation between the threshold used in the Chi-Square test, the size of the model built and the relative error of the value function of the induced policy with respect to the optimal value. We show that, on stochastic problems, one can tune the threshold so as to generate both a compact model and an efficient policy. Then, we show that SPITI, while keeping its model compact, uses the generalization property of its learning method to perform better than a stochastic classical tabular algorithm in large RL problem with an unknown structure. We also introduce a new measure based on Chi-Square to qualify the accuracy of the model learned by SPITI. We qualitatively show that the generalization property in SPITI within the FMDP framework may prevent an exponential growth of the time required to learn the structure of large stochastic RL problems.

We consider apprenticeship learning, i.e., having an agent learn a task by observing an expert demonstrating the task in a partially observable environment when the model of the environment is uncertain. This setting is useful in applications where the explicit modeling of the environment is difficult, such as a dialogue system. We show that we can extract information about the environment model by inferring action selection process behind the demonstration, under the assumption that the expert is choosing optimal actions based on knowledge of the true model of the target environment. Proposed algorithms can achieve more accurate estimates of POMDP parameters and better policies from a short demonstration, compared to methods that learns only from the reaction from the environment.

We observe that certain large-clique graph triangulations can be useful to reduce both computational and space requirements when making queries on mixed stochastic/deterministic graphical models. We demonstrate that many of these large-clique triangulations are non-minimal and are thus unattainable via the variable elimination algorithm. We introduce ancestral pairs as the basis for novel triangulation heuristics and prove that no more than the addition of edges between ancestral pairs need be considered when searching for state space optimal triangulations in such graphs. Empirical results on random and real world graphs show that the resulting triangulations that yield significant speedups are almost always non-minimal. We also give an algorithm and correctness proof for determining if a triangulation can be obtained via elimination, and we show that the decision problem associated with finding optimal state space triangulations in this mixed stochastic/deterministic setting is NP-complete.

We consider the problem of designing a sparse Gaussian process classifier (SGPC) that generalizes well. Viewing SGPC design as constructing an additive model like in boosting, we present an efficient and effective SGPC design method to perform a stage-wise optimization of a predictive loss function. We introduce new methods for two key components viz., site parameter estimation and basis vector selection in any SGPC design. The proposed adaptive sampling based basis vector selection method aids in achieving improved generalization performance at a reduced computational cost. This method can also be used in conjunction with any other site parameter estimation methods. It has similar computational and storage complexities as the well-known information vector machine and is suitable for large datasets. The hyperparameters can be determined by optimizing a predictive loss function. The experimental results show better generalization performance of the proposed basis vector selection method on several benchmark datasets, particularly for relatively smaller basis vector set sizes or on difficult datasets.

Optimization algorithms are normally influenced by meta-heuristic approach. In recent years several hybrid methods for optimization are developed to find out a better solution. The proposed work using meta-heuristic Nature Inspired algorithm is applied with back-propagation method to train a feed-forward neural network. Firefly algorithm is a nature inspired meta-heuristic algorithm, and it is incorporated into back-propagation algorithm to achieve fast and improved convergence rate in training feed-forward neural network. The proposed technique is tested over some standard data set. It is found that proposed method produces an improved convergence within very few iteration. This performance is also analyzed and compared to genetic algorithm based back-propagation. It is observed that proposed method consumes less time to converge and providing improved convergence rate with minimum feed-forward neural network design.