The L1-regularized Gaussian maximum likelihood estimator (MLE) has been shown to have strong statistical guarantees in recovering a sparse inverse covariance matrix, or alternatively the underlying graph structure of a Gaussian Markov Random Field, from very limited samples. We propose a novel algorithm for solving the resulting optimization problem which is a regularized log-determinant program. In contrast to recent state-of-the-art methods that largely use first order gradient information, our algorithm is based on Newton's method and employs a quadratic approximation, but with some modifications that leverage the structure of the sparse Gaussian MLE problem. We show that our method is superlinearly convergent, and present experimental results using synthetic and real-world application data that demonstrate the considerable improvements in performance of our method when compared to other state-of-the-art methods.

It has always been a great challenge for clustering algorithms to automatically determine the cluster numbers according to the distribution of datasets. Several approaches have been proposed to address this issue, including the recent promising work which incorporate Bayesian Nonparametrics into the $k$-means clustering procedure. This approach shows simplicity in implementation and solidity in theory, while it also provides a feasible way to inference in large scale datasets. However, several problems remains unsolved in this pioneering work, including the power-law data applicability, mechanism to merge centers to avoid the over-fitting problem, clustering order problem, e.t.c.. To address these issues, the Pitman-Yor Process based k-means (namely \emph{pyp-means}) is proposed in this paper. Taking advantage of the Pitman-Yor Process, \emph{pyp-means} treats clusters differently by dynamically and adaptively changing the threshold to guarantee the generation of power-law clustering results. Also, one center agglomeration procedure is integrated into the implementation to be able to merge small but close clusters and then adaptively determine the cluster number. With more discussion on the clustering order, the convergence proof, complexity analysis and extension to spectral clustering, our approach is compared with traditional clustering algorithm and variational inference methods. The advantages and properties of pyp-means are validated by experiments on both synthetic datasets and real world datasets.

Directional and pairwise measurements are often used to model inter-relationships in a social network setting. The Mixed-Membership Stochastic Blockmodel (MMSB) was a seminal work in this area, and many of its capabilities were extended since then. In this paper, we propose the \emph{Dynamic Infinite Mixed-Membership stochastic blockModel (DIM3)}, a generalised framework that extends the existing work to a potentially infinite number of communities and mixture memberships for each of the network's nodes. This model is in a dynamic setting, where additional model parameters are introduced to reflect the degree of persistence between one's memberships at consecutive times. Accordingly, two effective posterior sampling strategies and their results are presented using both synthetic and real data.

Bayesian Reinforcement Learning (RL) is capable of not only incorporating domain knowledge, but also solving the exploration-exploitation dilemma in a natural way. As Bayesian RL is intractable except for special cases, previous work has proposed several approximation methods. However, these methods are usually too sensitive to parameter values, and finding an acceptable parameter setting is practically impossible in many applications. In this paper, we propose a new algorithm that greedily approximates Bayesian RL to achieve robustness in parameter space. We show that for a desired learning behavior, our proposed algorithm has a polynomial sample complexity that is lower than those of existing algorithms. We also demonstrate that the proposed algorithm naturally outperforms other existing algorithms when the prior distributions are not significantly misleading. On the other hand, the proposed algorithm cannot handle greatly misspecified priors as well as the other algorithms can. This is a natural consequence of the fact that the proposed algorithm is greedier than the other algorithms. Accordingly, we discuss a way to select an appropriate algorithm for different tasks based on the algorithms' greediness. We also introduce a new way of simplifying Bayesian planning, based on which future work would be able to derive new algorithms.

The problem of minimizing a continuously differentiable convex function over an intersection of closed convex sets is ubiquitous in applied mathematics. It is particularly interesting when it is easy to project onto each separate set, but nontrivial to project onto their intersection. Algorithms based on Newton's method such as the interior point method are viable for small to medium-scale problems. However, modern applications in statistics, engineering, and machine learning are posing problems with potentially tens of thousands of parameters or more. We revisit this convex programming problem and propose an algorithm that scales well with dimensionality. Our proposal is an instance of a sequential unconstrained minimization technique and revolves around three ideas: the majorization-minimization (MM) principle, the classical penalty method for constrained optimization, and quasi-Newton acceleration of fixed-point algorithms. The performance of our distance majorization algorithms is illustrated in several applications.

We consider the stochastic approximation problem where a convex function has to be minimized, given only the knowledge of unbiased estimates of its gradients at certain points, a framework which includes machine learning methods based on the minimization of the empirical risk. We focus on problems without strong convexity, for which all previously known algorithms achieve a convergence rate for function values of O(1/n^{1/2}). We consider and analyze two algorithms that achieve a rate of O(1/n) for classical supervised learning problems. For least-squares regression, we show that averaged stochastic gradient descent with constant step-size achieves the desired rate. For logistic regression, this is achieved by a simple novel stochastic gradient algorithm that (a) constructs successive local quadratic approximations of the loss functions, while (b) preserving the same running time complexity as stochastic gradient descent. For these algorithms, we provide a non-asymptotic analysis of the generalization error (in expectation, and also in high probability for least-squares), and run extensive experiments on standard machine learning benchmarks showing that they often outperform existing approaches.

Many natural signals exhibit a sparse representation, whenever a suitable describing model is given. Here, a linear generative model is considered, where many sparsity-based signal processing techniques rely on such a simplified model. As this model is often unknown for many classes of the signals, we need to select such a model based on the domain knowledge or using some exemplar signals. This paper presents a new exemplar based approach for the linear model (called the dictionary) selection, for such sparse inverse problems. The problem of dictionary selection, which has also been called the dictionary learning in this setting, is first reformulated as a joint sparsity model. The joint sparsity model here differs from the standard joint sparsity model as it considers an overcompleteness in the representation of each signal, within the range of selected subspaces. The new dictionary selection paradigm is examined with some synthetic and realistic simulations.

Temporal-difference (TD) learning is one of the most successful and broadly applied solutions to the reinforcement learning problem; it has been used to achieve master-level play in chess, checkers and backgammon. Monte-Carlo tree search is a recent algorithm for simulation-based search, which has been used to achieve master-level play in Go. We have introduced a new approach to high-performance planning. Our method, TD search, combines TD learning with simulation-based search. Like Monte-Carlo tree search, value estimates are updated by learning online from simulated experience. Like TD learning, it uses value function approximation and bootstrapping to efficiently generalise between related states. We applied TD search to the game of 9x9 Go, using a million binary features matching simple patterns of stones. Without any explicit search tree, our approach outperformed a vanilla Monte-Carlo tree search with the same number of simulations. When combined with a simple alpha-beta search, our program also outperformed all traditional (pre-Monte-Carlo) search and machine learning programs on the 9x9 Computer Go Server.

In this article we address the problem of realizing a service-providing reasoning infrastructure for pro-active humanassistance in intelligent environments. We propose SAM, an architecture which leverages temporal knowledge represented asrelations in Allen’s interval algebra and constraint-based temporal planning techniques. SAM provides two key capabilities forcontextualized service provision: human activity recognition and planning for controlling pervasive actuation devices. Whiledrawing inspiration from several state-of-the-art approaches, SAM provides a unique feature which has thus far not been addressed in the literature, namely the seamless integration of these two key capabilities. It does so by leveraging a constraint-basedreasoning paradigm whereby both requirements for recognition and for planning/execution are represented as constraints andreasoned upon continuously.

In this article we address the problem of realizing a service-providing reasoning infrastructure for pro-active humanassistance in intelligent environments. We propose SAM, an architecture which leverages temporal knowledge represented asrelations in Allen’s interval algebra and constraint-based temporal planning techniques. SAM provides two key capabilities forcontextualized service provision: human activity recognition and planning for controlling pervasive actuation devices. Whiledrawing inspiration from several state-of-the-art approaches, SAM provides a unique feature which has thus far not been addressed in the literature, namely the seamless integration of these two key capabilities. It does so by leveraging a constraint-basedreasoning paradigm whereby both requirements for recognition and for planning/execution are represented as constraints andreasoned upon continuously.