In the field of domain-independent planning, several powerful planners implementing different techniques have been developed. However, no one of these systems outperforms all others in every known benchmark domain. In this work, we propose a multi-planner approach that automatically configures a portfolio of planning techniques for each given domain. The configuration process for a given domain uses a set of training instances to: (i) compute and analyze some alternative sets of macro-actions for each planner in the portfolio identifying a (possibly empty) useful set, (ii) select a cluster of planners, each one with the identified useful set of macro-actions, that is expected to perform best, and (iii) derive some additional information for configuring the execution scheduling of the selected planners at planning time. The resulting planning system, called PbP (Portfolio- based Planner), has two variants focusing on speed and plan quality. Different versions of PbP entered and won the learning track of the sixth and seventh International Planning Competitions. In this paper, we experimentally analyze PbP considering planning speed and plan quality in depth. We provide a collection of results that help to understand PbPs behavior, and demonstrate the effectiveness of our approach to configuring a portfolio of planners with macro-actions.

Credal networks are graph-based statistical models whose parameters take values in a set, instead of being sharply specified as in traditional statistical models (e.g., Bayesian networks). The computational complexity of inferences on such models depends on the irrelevance/independence concept adopted. In this paper, we study inferential complexity under the concepts of epistemic irrelevance and strong independence. We show that inferences under strong independence are NP-hard even in trees with binary variables except for a single ternary one. We prove that under epistemic irrelevance the polynomial-time complexity of inferences in credal trees is not likely to extend to more general models (e.g., singly connected topologies). These results clearly distinguish networks that admit efficient inferences and those where inferences are most likely hard, and settle several open questions regarding their computational complexity. We show that these results remain valid even if we disallow the use of zero probabilities. We also show that the computation of bounds on the probability of the future state in a hidden Markov model is the same whether we assume epistemic irrelevance or strong independence, and we prove a similar result for inference in naive Bayes structures. These inferential equivalences are important for practitioners, as hidden Markov models and naive Bayes structures are used in real applications of imprecise probability.

Variable (feature, gene, model, which we use interchangeably) selections for regression with high-dimensional BIGDATA have found many applications in bioinformatics, computational biology, image processing, and engineering. One appealing approach is the L0 regularized regression which penalizes the number of nonzero features in the model directly. L0 is known as the most essential sparsity measure and has nice theoretical properties, while the popular L1 regularization is only a best convex relaxation of L0. Therefore, it is natural to expect that L0 regularized regression performs better than LASSO. However, it is well-known that L0 optimization is NP-hard and computationally challenging. Instead of solving the L0 problems directly, most publications so far have tried to solve an approximation problem that closely resembles L0 regularization. In this paper, we propose an efficient EM algorithm (L0EM) that directly solves the L0 optimization problem. $L_0$EM is efficient with high dimensional data. It also provides a natural solution to all Lp p in [0,2] problems. The regularized parameter can be either determined through cross-validation or AIC and BIC. Theoretical properties of the L0-regularized estimator are given under mild conditions that permit the number of variables to be much larger than the sample size. We demonstrate our methods through simulation and high-dimensional genomic data. The results indicate that L0 has better performance than LASSO and L0 with AIC or BIC has similar performance as computationally intensive cross-validation. The proposed algorithms are efficient in identifying the non-zero variables with less-bias and selecting biologically important genes and pathways with high dimensional BIGDATA.

Motivation: Algorithms that discover variables which are causally related to a target may inform the design of experiments. With observational gene expression data, many methods discover causal variables by measuring each variable's degree of statistical dependence with the target using dependence measures (DMs). However, other methods measure each variable's ability to explain the statistical dependence between the target and the remaining variables in the data using conditional dependence measures (CDMs), since this strategy is guaranteed to find the target's direct causes, direct effects, and direct causes of the direct effects in the infinite sample limit. In this paper, we design a new algorithm in order to systematically compare the relative abilities of DMs and CDMs in discovering causal variables from gene expression data. Results: The proposed algorithm using a CDM is sample efficient, since it consistently outperforms other state-of-the-art local causal discovery algorithms when samples sizes are small. However, the proposed algorithm using a CDM outperforms the proposed algorithm using a DM only when sample sizes are above several hundred. These results suggest that accurate causal discovery from gene expression data using current CDM-based algorithms requires datasets with at least several hundred samples. Availability: The proposed algorithm is freely available at https://github.com/ericstrobl/DvCD.

Scaling feature values is an important step in numerous machine learning tasks. Different features can have different value ranges and some form of a feature scaling is often required in order to learn an accurate classifier. However, feature scaling is conducted as a preprocessing task prior to learning. This is problematic in an online setting because of two reasons. First, it might not be possible to accurately determine the value range of a feature at the initial stages of learning when we have observed only a few number of training instances. Second, the distribution of data can change over the time, which render obsolete any feature scaling that we perform in a pre-processing step. We propose a simple but an effective method to dynamically scale features at train time, thereby quickly adapting to any changes in the data stream. We compare the proposed dynamic feature scaling method against more complex methods for estimating scaling parameters using several benchmark datasets for binary classification. Our proposed feature scaling method consistently outperforms more complex methods on all of the benchmark datasets and improves classification accuracy of a state-of-the-art online binary classifier algorithm.

We consider the problem of sparse coding, where each sample consists of a sparse linear combination of a set of dictionary atoms, and the task is to learn both the dictionary elements and the mixing coefficients. Alternating minimization is a popular heuristic for sparse coding, where the dictionary and the coefficients are estimated in alternate steps, keeping the other fixed. Typically, the coefficients are estimated via $\ell_1$ minimization, keeping the dictionary fixed, and the dictionary is estimated through least squares, keeping the coefficients fixed. In this paper, we establish local linear convergence for this variant of alternating minimization and establish that the basin of attraction for the global optimum (corresponding to the true dictionary and the coefficients) is $\order{1/s^2}$, where $s$ is the sparsity level in each sample and the dictionary satisfies RIP. Combined with the recent results of approximate dictionary estimation, this yields provable guarantees for exact recovery of both the dictionary elements and the coefficients, when the dictionary elements are incoherent.

We propose a general algorithm for approximating nonstandard Bayesian posterior distributions. The algorithm minimizes the Kullback-Leibler divergence of an approximating distribution to the intractable posterior distribution. Our method can be used to approximate any posterior distribution, provided that it is given in closed form up to the proportionality constant. The approximation can be any distribution in the exponential family or any mixture of such distributions, which means that it can be made arbitrarily precise. Several examples illustrate the speed and accuracy of our approximation method in practice.

We introduce kLog, a novel approach to statistical relational learning. Unlike standard approaches, kLog does not represent a probability distribution directly. It is rather a language to perform kernel-based learning on expressive logical and relational representations. kLog allows users to specify learning problems declaratively. It builds on simple but powerful concepts: learning from interpretations, entity/relationship data modeling, logic programming, and deductive databases. Access by the kernel to the rich representation is mediated by a technique we call graphicalization: the relational representation is first transformed into a graph --- in particular, a grounded entity/relationship diagram. Subsequently, a choice of graph kernel defines the feature space. kLog supports mixed numerical and symbolic data, as well as background knowledge in the form of Prolog or Datalog programs as in inductive logic programming systems. The kLog framework can be applied to tackle the same range of tasks that has made statistical relational learning so popular, including classification, regression, multitask learning, and collective classification. We also report about empirical comparisons, showing that kLog can be either more accurate, or much faster at the same level of accuracy, than Tilde and Alchemy. kLog is GPLv3 licensed and is available at http://klog.dinfo.unifi.it along with tutorials.

It has been demonstrated earlier that universal computation is 'almost surely' chaotic. Machine learning is a form of computational fixed point iteration, iterating over the computable function space. We showcase some properties of this iteration, and establish in general that the iteration is 'almost surely' of chaotic nature. This theory explains the observation in the counter intuitive properties of deep learning methods. This paper demonstrates that these properties are going to be universal to any learning method.

We review the history of the automation of mathematical induction