This paper introduces a multi-period inspector scheduling problem (MPISP), which is a new variant of the multi-trip vehicle routing problem with time windows (VRPTW). In the MPISP, each inspector is scheduled to perform a route in a given multi-period planning horizon. At the end of each period, each inspector is not required to return to the depot but has to stay at one of the vertices for recuperation. If the remaining time of the current period is insufficient for an inspector to travel from his/her current vertex $A$ to a certain vertex B, he/she can choose either waiting at vertex A until the start of the next period or traveling to a vertex C that is closer to vertex B. Therefore, the shortest transit time between any vertex pair is affected by the length of the period and the departure time. We first describe an approach of computing the shortest transit time between any pair of vertices with an arbitrary departure time. To solve the MPISP, we then propose several local search operators adapted from classical operators for the VRPTW and integrate them into a tabu search framework. In addition, we present a constrained knapsack model that is able to produce an upper bound for the problem. Finally, we evaluate the effectiveness of our algorithm with extensive experiments based on a set of test instances. Our computational results indicate that our approach generates high-quality solutions.

We consider the problem of learning the canonical parameters specifying an undirected graphical model (Markov random field) from the mean parameters. For graphical models representing a minimal exponential family, the canonical parameters are uniquely determined by the mean parameters, so the problem is feasible in principle. The goal of this paper is to investigate the computational feasibility of this statistical task. Our main result shows that parameter estimation is in general intractable: no algorithm can learn the canonical parameters of a generic pair-wise binary graphical model from the mean parameters in time bounded by a polynomial in the number of variables (unless RP = NP). Indeed, such a result has been believed to be true (see the monograph by Wainwright and Jordan (2008)) but no proof was known. Our proof gives a polynomial time reduction from approximating the partition function of the hard-core model, known to be hard, to learning approximate parameters. Our reduction entails showing that the marginal polytope boundary has an inherent repulsive property, which validates an optimization procedure over the polytope that does not use any knowledge of its structure (as required by the ellipsoid method and others).

The Infinite Relational Model (IRM) is a probabilistic model for relational data clustering that partitions objects into clusters based on observed relationships. This paper presents Averaged CVB (ACVB) solutions for IRM, convergence-guaranteed and practically useful fast Collapsed Variational Bayes (CVB) inferences. We first derive ordinary CVB and CVB0 for IRM based on the lower bound maximization. CVB solutions yield deterministic iterative procedures for inferring IRM given the truncated number of clusters. Our proposal includes CVB0 updates of hyperparameters including the concentration parameter of the Dirichlet Process, which has not been studied in the literature. To make the CVB more practically useful, we further study the CVB inference in two aspects. First, we study the convergence issues and develop a convergence-guaranteed algorithm for any CVB-based inferences called ACVB, which enables automatic convergence detection and frees non-expert practitioners from difficult and costly manual monitoring of inference processes. Second, we present a few techniques for speeding up IRM inferences. In particular, we describe the linear time inference of CVB0, allowing the IRM for larger relational data uses. The ACVB solutions of IRM showed comparable or better performance compared to existing inference methods in experiments, and provide deterministic, faster, and easier convergence detection.

Statistical tests that compare classification algorithms are univariate and use a single performance measure, e.g., misclassification error, $F$ measure, AUC, and so on. In multivariate tests, comparison is done using multiple measures simultaneously. For example, error is the sum of false positives and false negatives and a univariate test on error cannot make a distinction between these two sources, but a 2-variate test can. Similarly, instead of combining precision and recall in $F$ measure, we can have a 2-variate test on (precision, recall). We use Hotelling's multivariate $T^2$ test for comparing two algorithms, and when we have three or more algorithms we use the multivariate analysis of variance (MANOVA) followed by pairwise post hoc tests. In our experiments, we see that multivariate tests have higher power than univariate tests, that is, they can detect differences that univariate tests cannot. We also discuss how multivariate analysis allows us to automatically extract performance measures that best distinguish the behavior of multiple algorithms.

Agent programming is mostly a symbolic discipline and, as such, draws little benefits from probabilistic areas as machine learning and graphical models. However, the greatest objective of agent research is the achievement of autonomy in dynamical and complex environments --- a goal that implies embracing uncertainty and therefore the entailed representations, algorithms and techniques. This paper proposes an innovative and conflict free two layer approach to agent programming that uses already established methods and tools from both symbolic and probabilistic artificial intelligence. Moreover, this framework is illustrated by means of a widely used agent programming example, GoldMiners.

Covariance matrix estimation is a fundamental problem in the field of statistical signal processing. Many algorithms for detection and inference rely on accurate covariance estimators [1, 2]. The problem is well understood in the Gaussian unstructured case. But becomes significantly harder when the underlying distribution is non-Gaussian, for example in elliptical distributions, and when there is prior knowledge on the structure. In this paper, we propose a unified framework for covariance estimation in elliptical distributions with general convex structure. Over the last years there was a great interest in covariance estimation with known structure. The motivation to these works is that in many modern applications the dimension of the underlying distribution is large and there are not enough samples to estimate it precisely without additional structure hypotheses. The prior information on the structure reduces the number of degrees of freedom in the model and allows accurate estimation with a small number of samples. This is clearly true when the structure is exact, but also when it is approximate due to the well known bias-variance tradeoff.

We study inference and learning based on a sparse coding model with `spike-and-slab' prior. As in standard sparse coding, the model used assumes independent latent sources that linearly combine to generate data points. However, instead of using a standard sparse prior such as a Laplace distribution, we study the application of a more flexible `spike-and-slab' distribution which models the absence or presence of a source's contribution independently of its strength if it contributes. We investigate two approaches to optimize the parameters of spike-and-slab sparse coding: a novel truncated EM approach and, for comparison, an approach based on standard factored variational distributions. The truncated approach can be regarded as a variational approach with truncated posteriors as variational distributions. In applications to source separation we find that both approaches improve the state-of-the-art in a number of standard benchmarks, which argues for the use of `spike-and-slab' priors for the corresponding data domains. Furthermore, we find that the truncated EM approach improves on the standard factored approach in source separation tasks$-$which hints to biases introduced by assuming posterior independence in the factored variational approach. Likewise, on a standard benchmark for image denoising, we find that the truncated EM approach improves on the factored variational approach. While the performance of the factored approach saturates with increasing numbers of hidden dimensions, the performance of the truncated approach improves the state-of-the-art for higher noise levels.

This paper aims at constructing a good graph for discovering intrinsic data structures in a semi-supervised learning setting. Firstly, we propose to build a non-negative low-rank and sparse (referred to as NNLRS) graph for the given data representation. Specifically, the weights of edges in the graph are obtained by seeking a nonnegative low-rank and sparse matrix that represents each data sample as a linear combination of others. The so-obtained NNLRS-graph can capture both the global mixture of subspaces structure (by the low rankness) and the locally linear structure (by the sparseness) of the data, hence is both generative and discriminative. Secondly, as good features are extremely important for constructing a good graph, we propose to learn the data embedding matrix and construct the graph jointly within one framework, which is termed as NNLRS with embedded features (referred to as NNLRS-EF). Extensive experiments on three publicly available datasets demonstrate that the proposed method outperforms the state-of-the-art graph construction method by a large margin for both semi-supervised classification and discriminative analysis, which verifies the effectiveness of our proposed method.

Recently, there has been a burst in the number of research projects on human computation via crowdsourcing. Multiple choice (or labeling) questions could be referred to as a common type of problem which is solved by this approach. As an application, crowd labeling is applied to find true labels for large machine learning datasets. Since crowds are not necessarily experts, the labels they provide are rather noisy and erroneous. This challenge is usually resolved by collecting multiple labels for each sample, and then aggregating them to estimate the true label. Although the mechanism leads to high-quality labels, it is not actually cost-effective. As a result, efforts are currently made to maximize the accuracy in estimating true labels, while fixing the number of acquired labels. This paper surveys methods to aggregate redundant crowd labels in order to estimate unknown true labels. It presents a unified statistical latent model where the differences among popular methods in the field correspond to different choices for the parameters of the model. Afterwards, algorithms to make inference on these models will be surveyed. Moreover, adaptive methods which iteratively collect labels based on the previously collected labels and estimated models will be discussed. In addition, this paper compares the distinguished methods, and provides guidelines for future work required to address the current open issues.

We consider the problem of belief tracking in a planning setting where states are valuations over a set of variables that are partially observable, and beliefs stand for the sets of states that are possible. While the problem is intractable in the worst case, it has been recently shown that in deterministic conformant and contingent problems, belief tracking is exponential in a width parameter that is often bounded and small. In this work, we extend these results in two ways. First, we introduce a width notion that applies to non-deterministic problems as well, develop a factored belief tracking algorithm that is exponential in the problem width, and show how it applies to existing benchmarks. Second, we introduce a meaningful, powerful, and sound approximation scheme, beam tracking, that is exponential in a smaller parameter, the problem causal width, and has much broader applicability. We illustrate the value of this algorithm over large instances of problems such as Battleship, Minesweeper, and Wumpus, where it yields state-of-the-art performance in real-time.