We present an algorithm for finding a chordal Markov network that maximizes any given decomposable scoring function. The algorithm is based on a recursive characterization of clique trees, and it runs in O(4^n) time for n vertices. On an eight-vertex benchmark instance, our implementation turns out to be about ten million times faster than a recently proposed, constraint satisfaction based algorithm (Corander et al., NIPS 2013). Within a few hours, it is able to solve instances up to 18 vertices, and beyond if we restrict the maximum clique size. We also study the performance of a recent integer linear programming algorithm (Bartlett and Cussens, UAI 2013). Our results suggest that, unless we bound the clique sizes, currently only the dynamic programming algorithm is guaranteed to solve instances with around 15 or more vertices.

We present an algorithm for finding a chordal Markov network that maximizes any given decomposable scoring function. The algorithm is based on a recursive characterization of clique trees, and it runs in O(4 n) time for n vertices. On an eight-vertex benchmark instance, our implementation turns out to be about ten million times faster than a recently proposed, constraint satisfaction based algorithm (Corander et al., NIPS 2013). Within a few hours, it is able to solve instances up to 18 vertices, and beyond if we restrict the maximum clique size. We also study the performance of a recent integer linear programming algorithm (Bartlett and Cussens, UAI 2013).

Markov Decision Processes (MDPs) are extremely useful for modeling and solving sequential decision making problems. Graph-based MDPs provide a compact representation for MDPs with large numbers of random variables. However, the complexity of exactly solving a graph-based MDP usually grows exponentially in the number of variables, which limits their application. We present a new variational framework to describe and solve the planning problem of MDPs, and derive both exact and approximate planning algorithms. In particular, by exploiting the graph structure of graph-based MDPs, we propose a factored variational value iteration algorithm in which the value function is first approximated by the multiplication of local-scope value functions, then solved by minimizing a Kullback-Leibler (KL) divergence. The KL divergence is optimized using the belief propagation algorithm, with complexity exponential in only the cluster size of the graph. Experimental comparison on different models shows that our algorithm outperforms existing approximation algorithms at finding good policies.

In the negative perceptron problem we are given $n$ data points $({\boldsymbol x}_i,y_i)$, where ${\boldsymbol x}_i$ is a $d$-dimensional vector and $y_i\in\{+1,-1\}$ is a binary label. The data are not linearly separable and hence we content ourselves to find a linear classifier with the largest possible \emph{negative} margin. In other words, we want to find a unit norm vector ${\boldsymbol \theta}$ that maximizes $\min_{i\le n}y_i\langle {\boldsymbol \theta},{\boldsymbol x}_i\rangle$. This is a non-convex optimization problem (it is equivalent to finding a maximum norm vector in a polytope), and we study its typical properties under two random models for the data. We consider the proportional asymptotics in which $n,d\to \infty$ with $n/d\to\delta$, and prove upper and lower bounds on the maximum margin $\kappa_{\text{s}}(\delta)$ or -- equivalently -- on its inverse function $\delta_{\text{s}}(\kappa)$. In other words, $\delta_{\text{s}}(\kappa)$ is the overparametrization threshold: for $n/d\le \delta_{\text{s}}(\kappa)-\varepsilon$ a classifier achieving vanishing training error exists with high probability, while for $n/d\ge \delta_{\text{s}}(\kappa)+\varepsilon$ it does not. Our bounds on $\delta_{\text{s}}(\kappa)$ match to the leading order as $\kappa\to -\infty$. We then analyze a linear programming algorithm to find a solution, and characterize the corresponding threshold $\delta_{\text{lin}}(\kappa)$. We observe a gap between the interpolation threshold $\delta_{\text{s}}(\kappa)$ and the linear programming threshold $\delta_{\text{lin}}(\kappa)$, raising the question of the behavior of other algorithms.

Recent breakthroughs in associative memories suggest that silicon memories are coming closer to human memories, especially for memristive Content Addressable Memories (CAMs) which are capable to read and write in analog values. However, the Program-Verify algorithm, the state-of-the-art memristor programming algorithm, requires frequent switching between verifying and programming memristor conductance, which brings many defects such as high dynamic power and long programming time. Here, we propose an analog feedback-controlled memristor programming circuit that makes use of a novel look-up table-based (LUT-based) programming algorithm. With the proposed algorithm, the programming and the verification of a memristor can be performed in a single-direction sequential process. Besides, we also integrated a single proposed programming circuit with eight analog CAM (aCAM) cells to build an aCAM array. We present SPICE simulations on TSMC 28nm process. The theoretical analysis shows that 1. A memristor conductance within an aCAM cell can be converted to an output boundary voltage in aCAM searching operations and 2. An output boundary voltage in aCAM searching operations can be converted to a programming data line voltage in aCAM programming operations. The simulation results of the proposed programming circuit prove the theoretical analysis and thus verify the feasibility to program memristors without frequently switching between verifying and programming the conductance. Besides, the simulation results of the proposed aCAM array show that the proposed programming circuit can be integrated into a large array architecture.

We consider the problem of generating optimal stochastic policies for Constrained Stochastic Shortest Path problems, which are a natural model for planning under uncertainty for resource-bounded agents with multiple competing objectives. While unconstrained SSPs enjoy a multitude of efficient heuristic search solution methods with the ability to focus on promising areas reachable from the initial state, the state of the art for constrained SSPs revolves around linear and dynamic programming algorithms which explore the entire state space. In this paper, we present i-dual, which, to the best of our knowledge, is the first heuristic search algorithm for constrained SSPs. To concisely represent constraints and efficiently decide their violation, i-dual operates in the space of dual variables describing the policy occupation measures. It does so while retaining the ability to use standard value function heuristics computed by well-known methods. Our experiments on a suite of PPDDL problems augmented with constraints show that these features enable i-dual to achieve up to two orders of magnitude improvement in run-time and memory over linear programming algorithms.

In diploid organisms, such as humans, each individual's genome is organized into pairs of chromosomes, each half inherited from each parent. When an individual is an offspring of biologically related parents, both chromosomes of the same pair can share identical segments, creating long stretches of consecutive homozygosity, known as runs of homozygosity (ROH). In the last decades, studies on the identification of ROH carried out in human populations have revealed the presence of ROH even in cosmopolitan non-inbred populations, disclosing an increment of inbreeding levels and the consequent reduction of genetic diversity of populations, which is proportional to the walking distance from Africa, as expected by the out-of-Africa model of human colonization (Ceballos et al., 2018; Kirin et al., 2010; Lemes et al., 2018; Leutenegger et al., 2011; Pemberton et al., 2012). The distribution of ROH along the chromosomes is very uneven, resulting in some genomic regions having significant absence (coldspots) or excess of ROH (ROH islands) (Ceballos et al., 2018). The mechanisms for the emergence of these regions are still under discussion. For example, there is evidence that ROH islands could represent regions that harbor genes target of positive selection since low-recombination regions commonly are locations of selective sweeps, in which a new beneficial mutation increases in frequency and becomes fixed, causing the overall reduction in genetic diversity of the region (Ceballos et al., 2018; Pemberton et al., 2012). To detect ROH and ROH islands, the genetic material of individuals from a given population is genotyped, and a set of single nucleotide polymorphisms (SNPs) is obtained. Each SNP entry is codified to 1 if that SNP belongs to an ROH for that individual and to 0 otherwise, where a marker is defined as belonging to an ROH for an individual if it is surrounded by a region with high frequency of homozygous SNPs.

We present an algorithm for finding a chordal Markov network that maximizes any given decomposable scoring function. The algorithm is based on a recursive characterization of clique trees, and it runs in O(4 n) time for n vertices. On an eight-vertex benchmark instance, our implementation turns out to be about ten million times faster than a recently proposed, constraint satisfaction based algorithm (Corander et al., NIPS 2013). Within a few hours, it is able to solve instances up to 18 vertices, and beyond if we restrict the maximum clique size. We also study the performance of a recent integer linear programming algorithm (Bartlett and Cussens, UAI 2013).

Markov Decision Processes (MDPs) are extremely useful for modeling and solving sequential decision making problems. Graph-based MDPs provide a compact representation for MDPs with large numbers of random variables. However, the complexity of exactly solving a graph-based MDP usually grows exponentially in the number of variables, which limits their application. We present a new varia-tional framework to describe and solve the planning problem of MDPs, and derive both exact and approximate planning algorithms. In particular, by exploiting the graph structure of graph-based MDPs, we propose a factored variational value iteration algorithm in which the value function is first approximated by the multiplication of local-scope value functions, then solved by minimizing a Kullback-Leibler (KL) divergence. The KL divergence is optimized using the belief propagation algorithm, with complexity exponential in only the cluster size of the graph. Experimental comparison on different models shows that our algorithm outperforms existing approximation algorithms at finding good policies.

Cardinality constraints or, more generally, weight constraints are well recognized as an important extension of answer-set programming. Clearly, all common algorithmic tasks related to programs with cardinality or weight constraints (PWCs) - like checking the consistency of a program - are intractable. Many intractable problems in the area of knowledge representation and reasoning have been shown to become tractable if the treewidth of the programs or formulas under consideration is bounded by some constant. The goal of this paper is to apply the notion of treewidth to PWCs and to identify tractable fragments. It will turn out that the straightforward application of treewidth to PWCs does not suffice to obtain tractability. However, by imposing further restrictions, tractability can be achieved.