Regularized linear regression under the $\ell_1$ penalty, such as the Lasso, has been shown to be effective in variable selection and sparse modeling. The sampling distribution of an $\ell_1$-penalized estimator $\hat{\beta}$ is hard to determine as the estimator is defined by an optimization problem that in general can only be solved numerically and many of its components may be exactly zero. Let $S$ be the subgradient of the $\ell_1$ norm of the coefficient vector $\beta$ evaluated at $\hat{\beta}$. We find that the joint sampling distribution of $\hat{\beta}$ and $S$, together called an augmented estimator, is much more tractable and has a closed-form density under a normal error distribution in both low-dimensional ($p\leq n$) and high-dimensional ($p>n$) settings. Given $\beta$ and the error variance $\sigma^2$, one may employ standard Monte Carlo methods, such as Markov chain Monte Carlo and importance sampling, to draw samples from the distribution of the augmented estimator and calculate expectations with respect to the sampling distribution of $\hat{\beta}$. We develop a few concrete Monte Carlo algorithms and demonstrate with numerical examples that our approach may offer huge advantages and great flexibility in studying sampling distributions in $\ell_1$-penalized linear regression. We also establish nonasymptotic bounds on the difference between the true sampling distribution of $\hat{\beta}$ and its estimator obtained by plugging in estimated parameters, which justifies the validity of Monte Carlo simulation from an estimated sampling distribution even when $p\gg n\to \infty$.

The verification of complex systems is generally based on proving the validity, or, dually, the satisfiability of a logical formula. A standard practice consists in translating the behavior of the system to be verified into a logical formula, and proving that the negation of the formula is unsatisfiable. These formulæ may be domain-specific, so that it is only necessary to test the satisfiability of the formula modulo some background theory, whence the name Satisfiability Modulo Theories problems, or SMT problems. If the formula is actually satisfiable, this means the system is not error-free, and any model can be viewed as a trace that generates an error. The models of a satisfiable formula can therefore help the designers of the system guess the origin of the errors and deduce how they can be corrected; this is the main reason for example why state-of-the-art SMT solvers feature automated model building tools (see for instance Caferra, Leitsch, and Peltier, 2004).

The dynamics of belief and knowledge is one of the major components of any autonomous system that should be able to incorporate new pieces of information. In order to apply the rationality result of belief dynamics theory to various practical problems, it should be generalized in two respects: first it should allow a certain part of belief to be declared as immutable; and second, the belief state need not be deductively closed. Such a generalization of belief dynamics, referred to as base dynamics, is presented in this paper, along with the concept of a generalized revision algorithm for knowledge bases (Horn or Horn logic with stratified negation). We show that knowledge base dynamics has an interesting connection with kernel change via hitting set and abduction. In this paper, we show how techniques from disjunctive logic programming can be used for efficient (deductive) database updates. The key idea is to transform the given database together with the update request into a disjunctive (datalog) logic program and apply disjunctive techniques (such as minimal model reasoning) to solve the original update problem. The approach extends and integrates standard techniques for efficient query answering and integrity checking. The generation of a hitting set is carried out through a hyper tableaux calculus and magic set that is focused on the goal of minimality. Keyword: AGM, Belief Revision, Knowledge Base Dynamics, Kernel Change, Abduction, Hyber Tableaux, Magic Set, View update, Update Propagation.

Learning Markov blanket (MB) structures has proven useful in performing feature selection, learning Bayesian networks (BNs), and discovering causal relationships. We present a formula for efficiently determining the number of MB structures given a target variable and a set of other variables. As expected, the number of MB structures grows exponentially. However, we show quantitatively that there are many fewer MB structures that contain the target variable than there are BN structures that contain it. In particular, the ratio of BN structures to MB structures appears to increase exponentially in the number of variables.

As large-scale theft of data from corporate servers is becoming increasingly common, it becomes interesting to examine alternatives to the paradigm of centralizing sensitive data into large databases. Instead, one could use cryptography and distributed computation so that sensitive data can be supplied and processed in encrypted form, and only the final result is made known. In this paper, we examine how such a paradigm can be used to implement constraint satisfaction, a technique that can solve a broad class of AI problems such as resource allocation, planning, scheduling, and diagnosis. Most previous work on privacy in constraint satisfaction only attempted to protect specific types of information, in particular the feasibility of particular combinations of decisions. We formalize and extend these restricted notions of privacy by introducing four types of private information, including the feasibility of decisions and the final decisions made, but also the identities of the participants and the topology of the problem. We present distributed algorithms that allow computing solutions to constraint satisfaction problems while maintaining these four types of privacy. We formally prove the privacy properties of these algorithms, and show experiments that compare their respective performance on benchmark problems.

In this paper we are going to introduce a new nearest neighbours based approach to clustering, and compare it with previous solutions; the resulting algorithm, which takes inspiration from both DBscan and minimum spanning tree approaches, is deterministic but proves simpler, faster and doesn't require to set in advance a value for k, the number of clusters.

In this paper, we study active learning of classifiers in an agnostic setting, where no assumptions are made on the true function that generates the labels. The learner has access to a large pool of unlabelled examples, and can interactively request labels for a small subset of these; the goal is to learn an accurate classifier in a pre-specified class with as few label queries as possible. Specifically, we are given a hypothesis class H and a target ǫ, and our aim is to find a binary classifier in H whose error is at most ǫ more than that of the best classifier in H, while minimizing the number of requested labels. There has been a large body of previous work on active learning; see the surveys by [Das11, Set10] for overviews. The main challenge in active learning is ensuring consistency in the agnostic setting while still maintaining low label complexity. In particular, a very natural approach to active learning is to view it as a generalization of binary search [FSST97, Das05, Now11]. While this strategy has been extended to several different noise models [Kää06, Now11, NJC13], it is generally inconsistent in the agnostic case [DH08]. The primary algorithm for agnostic active learning is called disagreement-based active learning.

The problem of low-rank matrix completion has recently generated a lot of interest leading to several results that offer exact solutions to the problem. However, in order to do so, these methods make assumptions that can be quite restrictive in practice. More specifically, the methods assume that: a) the observed indices are sampled uniformly at random, and b) for every new matrix, the observed indices are sampled afresh. In this work, we address these issues by providing a universal recovery guarantee for matrix completion that works for a variety of sampling schemes. In particular, we show that if the set of sampled indices come from the edges of a bipartite graph with large spectral gap (i.e. gap between the first and the second singular value), then the nuclear norm minimization based method exactly recovers all low-rank matrices that satisfy certain incoherence properties. Moreover, we also show that under certain stricter incoherence conditions, $O(nr^2)$ uniformly sampled entries are enough to recover any rank-$r$ $n\times n$ matrix, in contrast to the $O(nr\log n)$ sample complexity required by other matrix completion algorithms as well as existing analyses of the nuclear norm method.

An originally chaotic system can be controlled into various periodic dynamics. When it is implemented into a legged robot's locomotion control as a central pattern generator (CPG), sophisticated gait patterns arise so that the robot can perform various walking behaviors. However, such a single chaotic CPG controller has difficulties dealing with leg malfunction. Specifically, in the scenarios presented here, its movement permanently deviates from the desired trajectory. To address this problem, we extend the single chaotic CPG to multiple CPGs with learning. The learning mechanism is based on a simulated annealing algorithm. In a normal situation, the CPGs synchronize and their dynamics are identical. With leg malfunction or disability, the CPGs lose synchronization leading to independent dynamics. In this case, the learning mechanism is applied to automatically adjust the remaining legs' oscillation frequencies so that the robot adapts its locomotion to deal with the malfunction. As a consequence, the trajectory produced by the multiple chaotic CPGs resembles the original trajectory far better than the one produced by only a single CPG. The performance of the system is evaluated first in a physical simulation of a quadruped as well as a hexapod robot and finally in a real six-legged walking machine called AMOSII. The experimental results presented here reveal that using multiple CPGs with learning is an effective approach for adaptive locomotion generation where, for instance, different body parts have to perform independent movements for malfunction compensation.

We address the cold start problem in recommendation systems assuming no contextual information is available neither about users, nor items. We consider the case in which we only have access to a set of ratings of items by users. Most of the existing works consider a batch setting, and use cross-validation to tune parameters. The classical method consists in minimizing the root mean square error over a training subset of the ratings which provides a factorization of the matrix of ratings, interpreted as a latent representation of items and users. Our contribution in this paper is 5-fold. First, we explicit the issues raised by this kind of batch setting for users or items with very few ratings. Then, we propose an online setting closer to the actual use of recommender systems; this setting is inspired by the bandit framework. The proposed methodology can be used to turn any recommender system dataset (such as Netflix, MovieLens,...) into a sequential dataset. Then, we explicit a strong and insightful link between contextual bandit algorithms and matrix factorization; this leads us to a new algorithm that tackles the exploration/exploitation dilemma associated to the cold start problem in a strikingly new perspective. Finally, experimental evidence confirm that our algorithm is effective in dealing with the cold start problem on publicly available datasets. Overall, the goal of this paper is to bridge the gap between recommender systems based on matrix factorizations and those based on contextual bandits.