In this paper we study the estimation of changing trends in time-series using $\ell_1$ trend filtering. This method generalizes 1D Total Variation (TV) denoising for detection of step changes in means to detecting changes in trends, and it relies on a convex optimization problem for which there are very efficient numerical algorithms. It is known that TV denoising suffers from the so-called stair-case effect, which leads to detecting false change points. The objective of this paper is to show that $\ell_1$ trend filtering also suffers from a certain stair-case problem. The analysis is based on an interpretation of the dual variables of the optimization problem in the method as integrated random walk. We discuss consistency conditions for $\ell_1$ trend filtering, how to monitor their fulfillment, and how to modify the algorithm to avoid the stair-case false detection problem.

We develop estimation for potentially high-dimensional additive structural equation models. A key component of our approach is to decouple order search among the variables from feature or edge selection in a directed acyclic graph encoding the causal structure. We show that the former can be done with nonregularized (restricted) maximum likelihood estimation while the latter can be efficiently addressed using sparse regression techniques. Thus, we substantially simplify the problem of structure search and estimation for an important class of causal models. We establish consistency of the (restricted) maximum likelihood estimator for low- and high-dimensional scenarios, and we also allow for misspecification of the error distribution. Furthermore, we develop an efficient computational algorithm which can deal with many variables, and the new method's accuracy and performance is illustrated on simulated and real data.

Motivated by the recent applications of game-theoretical learning techniques to the design of distributed control systems, we study a class of control problems that can be formulated as potential games with continuous action sets, and we propose an actor-critic reinforcement learning algorithm that provably converges to equilibrium in this class of problems. The method employed is to analyse the learning process under study through a mean-field dynamical system that evolves in an infinite-dimensional function space (the space of probability distributions over the players' continuous controls). To do so, we extend the theory of finite-dimensional two-timescale stochastic approximation to an infinite-dimensional, Banach space setting, and we prove that the continuous dynamics of the process converge to equilibrium in the case of potential games. These results combine to give a provably-convergent learning algorithm in which players do not need to keep track of the controls selected by the other agents.

Recent development in developing humanoid robot poses new challenges to human-machine interaction communication. A major challenge is to develop robots that can behave like and interact with human in the most natural way possible. This paper proposes a system to develop a robot that can receive command, and talk to people in natural language. In addition, the robot can also be "trained" to become an expert in sepcific areas to provide expert advice to human-beings. Most important of all, the robot can display emotions through facial expression, speech and gesture so that the interaction process will become more comprehensive and compelling.

We study the model of projective simulation (PS), a novel approach to artificial intelligence based on stochastic processing of episodic memory which was recently introduced [H.J. Briegel and G. De las Cuevas. Sci. Rep. 2, 400, (2012)]. Here we provide a detailed analysis of the model and examine its performance, including its achievable efficiency, its learning times and the way both properties scale with the problems' dimension. In addition, we situate the PS agent in different learning scenarios, and study its learning abilities. A variety of new scenarios are being considered, thereby demonstrating the model's flexibility. Furthermore, to put the PS scheme in context, we compare its performance with those of Q-learning and learning classifier systems, two popular models in the field of reinforcement learning. It is shown that PS is a competitive artificial intelligence model of unique properties and strengths.

We consider the problem of reconstructing the graph underlying an Ising model from i.i.d. samples. Over the last fifteen years this problem has been of significant interest in the statistics, machine learning, and statistical physics communities, and much of the effort has been directed towards finding algorithms with low computational cost for various restricted classes of models. Nevertheless, for learning Ising models on general graphs with $p$ nodes of degree at most $d$, it is not known whether or not it is possible to improve upon the $p^{d}$ computation needed to exhaustively search over all possible neighborhoods for each node. In this paper we show that a simple greedy procedure allows to learn the structure of an Ising model on an arbitrary bounded-degree graph in time on the order of $p^2$. We make no assumptions on the parameters except what is necessary for identifiability of the model, and in particular the results hold at low-temperatures as well as for highly non-uniform models. The proof rests on a new structural property of Ising models: we show that for any node there exists at least one neighbor with which it has a high mutual information. This structural property may be of independent interest.

Lifted probabilistic inference algorithms have been successfully applied to a large number of symmetric graphical models. Unfortunately, the majority of real-world graphical models is asymmetric. This is even the case for relational representations when evidence is given. Therefore, more recent work in the community moved to making the models symmetric and then applying existing lifted inference algorithms. However, this approach has two shortcomings. First, all existing over-symmetric approximations require a relational representation such as Markov logic networks. Second, the induced symmetries often change the distribution significantly, making the computed probabilities highly biased. We present a framework for probabilistic sampling-based inference that only uses the induced approximate symmetries to propose steps in a Metropolis-Hastings style Markov chain. The framework, therefore, leads to improved probability estimates while remaining unbiased. Experiments demonstrate that the approach outperforms existing MCMC algorithms.

Knowledge Discovery in Databases is a complex process that involves many different data processing and learning operators. Today's Knowledge Discovery Support Systems can contain several hundred operators. A major challenge is to assist the user in designing workflows which are not only valid but also -- ideally -- optimize some performance measure associated with the user goal. In this paper we present such a system. The system relies on a meta-mining module which analyses past data mining experiments and extracts meta-mining models which associate dataset characteristics with workflow descriptors in view of workflow performance optimization. The meta-mining model is used within a data mining workflow planner, to guide the planner during the workflow planning. We learn the meta-mining models using a similarity learning approach, and extract the workflow descriptors by mining the workflows for generalized relational patterns accounting also for domain knowledge provided by a data mining ontology. We evaluate the quality of the data mining workflows that the system produces on a collection of real world datasets coming from biology and show that it produces workflows that are significantly better than alternative methods that can only do workflow selection and not planning.

We consider the least-squares regression problem and provide a detailed asymptotic analysis of the performance of averaged constant-step-size stochastic gradient descent (a.k.a. least-mean-squares). In the strongly-convex case, we provide an asymptotic expansion up to explicit exponentially decaying terms. Our analysis leads to new insights into stochastic approximation algorithms: (a) it gives a tighter bound on the allowed step-size; (b) the generalization error may be divided into a variance term which is decaying as O(1/n), independently of the step-size $\gamma$, and a bias term that decays as O(1/$\gamma$ 2 n 2); (c) when allowing non-uniform sampling, the choice of a good sampling density depends on whether the variance or bias terms dominate. In particular, when the variance term dominates, optimal sampling densities do not lead to much gain, while when the bias term dominates, we can choose larger step-sizes that leads to significant improvements.

In this paper we consider the problem of learning undirected graphical models from data generated according to the Glauber dynamics. The Glauber dynamics is a Markov chain that sequentially updates individual nodes (variables) in a graphical model and it is frequently used to sample from the stationary distribution (to which it converges given sufficient time). Additionally, the Glauber dynamics is a natural dynamical model in a variety of settings. This work deviates from the standard formulation of graphical model learning in the literature, where one assumes access to i.i.d. samples from the distribution. Much of the research on graphical model learning has been directed towards finding algorithms with low computational cost. As the main result of this work, we establish that the problem of reconstructing binary pairwise graphical models is computationally tractable when we observe the Glauber dynamics. Specifically, we show that a binary pairwise graphical model on $p$ nodes with maximum degree $d$ can be learned in time $f(d)p^2\log p$, for a function $f(d)$, using nearly the information-theoretic minimum number of samples.