arXiv subjects

Bart Selman

Publications and source records attributed to Bart Selman.

36 records · Page 2Linked to original sources

arXiv2016

Solving Marginal MAP Problems with NP Oracles and Parity Constraints

Arising from many applications at the intersection of decision making and machine learning, Marginal Maximum A Posteriori (Marginal MAP) Problems unify the two main classes of inference, namely maximization (optimization) and marginal inference (counting), and are believed to have higher complexity than both of them. We propose XOR_MMAP, a novel approach to solve the Marginal MAP Problem, which represents the intractable counting subproblem with queries to NP oracles, subject to additional parity constraints. XOR_MMAP provides a constant factor approximation to the Marginal MAP Problem, by encoding it as a single optimization in polynomial size of the original problem. We evaluate our approach in several machine learning and decision making applications, and show that our approach outperforms several state-of-the-art Marginal MAP solvers.

cs.AI↗

arXiv2016

Variable Elimination in the Fourier Domain

The ability to represent complex high dimensional probability distributions in a compact form is one of the key insights in the field of graphical models. Factored representations are ubiquitous in machine learning and lead to major computational advantages. We explore a different type of compact representation based on discrete Fourier representations, complementing the classical approach based on conditional independencies. We show that a large class of probabilistic graphical models have a compact Fourier representation. This theoretical result opens up an entirely new way of approximating a probability distribution. We demonstrate the significance of this approach by applying it to the variable elimination algorithm. Compared with the traditional bucket representation and other approximate inference algorithms, we obtain significant improvements.

cs.AI↗

arXiv2016

Watch-n-Patch: Unsupervised Learning of Actions and Relations

There is a large variation in the activities that humans perform in their everyday lives. We consider modeling these composite human activities which comprises multiple basic level actions in a completely unsupervised setting. Our model learns high-level co-occurrence and temporal relations between the actions. We consider the video as a sequence of short-term action clips, which contains human-words and object-words. An activity is about a set of action-topics and object-topics indicating which actions are present and which objects are interacting with. We then propose a new probabilistic model relating the words and the topics. It allows us to model long-range action relations that commonly exist in the composite activities, which is challenging in previous works. We apply our model to the unsupervised action segmentation and clustering, and to a novel application that detects forgotten actions, which we call action patching. For evaluation, we contribute a new challenging RGB-D activity video dataset recorded by the new Kinect v2, which contains several human daily activities as compositions of multiple actions interacting with different objects. Moreover, we develop a robotic system that watches people and reminds people by applying our action patching algorithm. Our robotic setup can be easily deployed on any assistive robot.

cs.CV↗

arXiv2015

Watch-Bot: Unsupervised Learning for Reminding Humans of Forgotten Actions

We present a robotic system that watches a human using a Kinect v2 RGB-D sensor, detects what he forgot to do while performing an activity, and if necessary reminds the person using a laser pointer to point out the related object. Our simple setup can be easily deployed on any assistive robot. Our approach is based on a learning algorithm trained in a purely unsupervised setting, which does not require any human annotations. This makes our approach scalable and applicable to variant scenarios. Our model learns the action/object co-occurrence and action temporal relations in the activity, and uses the learned rich relationships to infer the forgotten action and the related object. We show that our approach not only improves the unsupervised action segmentation and action cluster assignment performance, but also effectively detects the forgotten actions on a challenging human activity RGB-D video dataset. In robotic experiments, we show that our robot is able to remind people of forgotten actions successfully.

cs.RO↗

arXiv2014

Pattern Decomposition with Complex Combinatorial Constraints: Application to Materials Discovery

Identifying important components or factors in large amounts of noisy data is a key problem in machine learning and data mining. Motivated by a pattern decomposition problem in materials discovery, aimed at discovering new materials for renewable energy, e.g. for fuel and solar cells, we introduce CombiFD, a framework for factor based pattern decomposition that allows the incorporation of a-priori knowledge as constraints, including complex combinatorial constraints. In addition, we propose a new pattern decomposition algorithm, called AMIQO, based on solving a sequence of (mixed-integer) quadratic programs. Our approach considerably outperforms the state of the art on the materials discovery problem, scaling to larger datasets and recovering more precise and physically meaningful decompositions. We also show the effectiveness of our approach for enforcing background knowledge on other application domains.

cs.AI↗

arXiv2014

Synthesizing Manipulation Sequences for Under-Specified Tasks using Unrolled Markov Random Fields

Many tasks in human environments require performing a sequence of navigation and manipulation steps involving objects. In unstructured human environments, the location and configuration of the objects involved often change in unpredictable ways. This requires a high-level planning strategy that is robust and flexible in an uncertain environment. We propose a novel dynamic planning strategy, which can be trained from a set of example sequences. High level tasks are expressed as a sequence of primitive actions or controllers (with appropriate parameters). Our score function, based on Markov Random Field (MRF), captures the relations between environment, controllers, and their arguments. By expressing the environment using sets of attributes, the approach generalizes well to unseen scenarios. We train the parameters of our MRF using a maximum margin learning method. We provide a detailed empirical validation of our overall framework demonstrating successful plan strategies for a variety of tasks.

cs.RO↗

arXiv2014

On the Erdos Discrepancy Problem

According to the Erdős discrepancy conjecture, for any infinite $\pm 1$ sequence, there exists a homogeneous arithmetic progression of unbounded discrepancy. In other words, for any $\pm 1$ sequence $(x_1,x_2,...)$ and a discrepancy $C$, there exist integers $m$ and $d$ such that $|\sum_{i=1}^m x_{i \cdot d}| > C$. This is an $80$-year-old open problem and recent development proved that this conjecture is true for discrepancies up to $2$. Paul Erdős also conjectured that this property of unbounded discrepancy even holds for the restricted case of completely multiplicative sequences (CMSs), namely sequences $(x_1,x_2,...)$ where $x_{a \cdot b} = x_{a} \cdot x_{b}$ for any $a,b \geq 1$. The longest CMS with discrepancy $2$ has been proven to be of size $246$. In this paper, we prove that any completely multiplicative sequence of size $127,646$ or more has discrepancy at least $4$, proving the Erdős discrepancy conjecture for CMSs of discrepancies up to $3$. In addition, we prove that this bound is tight and increases the size of the longest known sequence of discrepancy $3$ from $17,000$ to $127,645$. Finally, we provide inductive construction rules as well as streamlining methods to improve the lower bounds for sequences of higher discrepancies.

cs.DM↗

arXiv2013

Optimization With Parity Constraints: From Binary Codes to Discrete Integration

Many probabilistic inference tasks involve summations over exponentially large sets. Recently, it has been shown that these problems can be reduced to solving a polynomial number of MAP inference queries for a model augmented with randomly generated parity constraints. By exploiting a connection with max-likelihood decoding of binary codes, we show that these optimizations are computationally hard. Inspired by iterative message passing decoding algorithms, we propose an Integer Linear Programming (ILP) formulation for the problem, enhanced with new sparsification techniques to improve decoding performance. By solving the ILP through a sequence of LP relaxations, we get both lower and upper bounds on the partition function, which hold with high probability and are much tighter than those obtained with variational methods.

cs.AI↗

arXiv2013

Taming the Curse of Dimensionality: Discrete Integration by Hashing and Optimization

Integration is affected by the curse of dimensionality and quickly becomes intractable as the dimensionality of the problem grows. We propose a randomized algorithm that, with high probability, gives a constant-factor approximation of a general discrete integral defined over an exponentially large set. This algorithm relies on solving only a small number of instances of a discrete combinatorial optimization problem subject to randomly generated parity constraints used as a hash function. As an application, we demonstrate that with a small number of MAP queries we can efficiently approximate the partition function of discrete graphical models, which can in turn be used, for instance, for marginal computation or model selection.

cs.LG↗

arXiv2013

Algorithm Portfolio Design: Theory vs. Practice

Stochastic algorithms are among the best for solving computationally hard search and reasoning problems. The runtime of such procedures is characterized by a random variable. Different algorithms give rise to different probability distributions. One can take advantage of such differences by combining several algorithms into a portfolio, and running them in parallel or interleaving them on a single processor. We provide a detailed evaluation of the portfolio approach on distributions of hard combinatorial search problems. We show under what conditions the protfolio approach can have a dramatic computational advantage over the best traditional methods.

cs.AI↗

arXiv2013

A Bayesian Approach to Tackling Hard Computational Problems

We are developing a general framework for using learned Bayesian models for decision-theoretic control of search and reasoningalgorithms. We illustrate the approach on the specific task of controlling both general and domain-specific solvers on a hard class of structured constraint satisfaction problems. A successful strategyfor reducing the high (and even infinite) variance in running time typically exhibited by backtracking search algorithms is to cut off and restart the search if a solution is not found within a certainamount of time. Previous work on restart strategies have employed fixed cut off values. We show how to create a dynamic cut off strategy by learning a Bayesian model that predicts the ultimate length of a trial based on observing the early behavior of the search algorithm. Furthermore, we describe the general conditions under which a dynamic restart strategy can outperform the theoretically optimal fixed strategy.

cs.AI↗

arXiv2012

From spin glasses to hard satisfiable formulas

We introduce a highly structured family of hard satisfiable 3-SAT formulas corresponding to an ordered spin-glass model from statistical physics. This model has provably "glassy" behavior; that is, it has many local optima with large energy barriers between them, so that local search algorithms get stuck and have difficulty finding the true ground state, i.e., the unique satisfying assignment. We test the hardness of our formulas with two Davis-Putnam solvers, Satz and zChaff, the recently introduced Survey Propagation (SP), and two local search algorithms, Walksat and Record-to-Record Travel (RRT). We compare our formulas to random 3-XOR-SAT formulas and to two other generators of hard satisfiable instances, the minimum disagreement parity formulas of Crawford et al., and Hirsch's hgen. For the complete solvers the running time of our formulas grows exponentially in sqrt(n), and exceeds that of random 3-XOR-SAT formulas for small problem sizes. SP is unable to solve our formulas with as few as 25 variables. For Walksat, our formulas appear to be harder than any other known generator of satisfiable instances. Finally, our formulas can be solved efficiently by RRT but only if the parameter d is tuned to the height of the barriers between local minima, and we use this parameter to measure the barrier heights in random 3-XOR-SAT formulas as well.

cond-mat.stat-mech↗

arXiv2012

Uniform Solution Sampling Using a Constraint Solver As an Oracle

We consider the problem of sampling from solutions defined by a set of hard constraints on a combinatorial space. We propose a new sampling technique that, while enforcing a uniform exploration of the search space, leverages the reasoning power of a systematic constraint solver in a black-box scheme. We present a series of challenging domains, such as energy barriers and highly asymmetric spaces, that reveal the difficulties introduced by hard constraints. We demonstrate that standard approaches such as Simulated Annealing and Gibbs Sampling are greatly affected, while our new technique can overcome many of these difficulties. Finally, we show that our sampling scheme naturally defines a new approximate model counting technique, which we empirically show to be very accurate on a range of benchmark problems.

cs.AI↗

arXiv2012

Survey Propagation Revisited

Survey propagation (SP) is an exciting new technique that has been remarkably successful at solving very large hard combinatorial problems, such as determining the satisfiability of Boolean formulas. In a promising attempt at understanding the success of SP, it was recently shown that SP can be viewed as a form of belief propagation, computing marginal probabilities over certain objects called covers of a formula. This explanation was, however, shortly dismissed by experiments suggesting that non-trivial covers simply do not exist for large formulas. In this paper, we show that these experiments were misleading: not only do covers exist for large hard random formulas, SP is surprisingly accurate at computing marginals over these covers despite the existence of many cycles in the formulas. This re-opens a potentially simpler line of reasoning for understanding SP, in contrast to some alternative lines of explanation that have been proposed assuming covers do not exist.

cs.AI↗

arXiv2012

Playing games against nature: optimal policies for renewable resource allocation

In this paper we introduce a class of Markov decision processes that arise as a natural model for many renewable resource allocation problems. Upon extending results from the inventory control literature, we prove that they admit a closed form solution and we show how to exploit this structure to speed up its computation. We consider the application of the proposed framework to several problems arising in very different domains, and as part of the ongoing effort in the emerging field of Computational Sustainability we discuss in detail its application to the Northern Pacific Halibut marine fishery. Our approach is applied to a model based on real world data, obtaining a policy with a guaranteed lower bound on the utility function that is structurally very different from the one currently employed.

cs.AI↗

arXiv2012

Understanding Sampling Style Adversarial Search Methods

UCT has recently emerged as an exciting new adversarial reasoning technique based on cleverly balancing exploration and exploitation in a Monte-Carlo sampling setting. It has been particularly successful in the game of Go but the reasons for its success are not well understood and attempts to replicate its success in other domains such as Chess have failed. We provide an in-depth analysis of the potential of UCT in domain-independent settings, in cases where heuristic values are available, and the effect of enhancing random playouts to more informed playouts between two weak minimax players. To provide further insights, we develop synthetic game tree instances and discuss interesting properties of UCT, both empirically and analytically.

cs.AI↗

arXiv2012

Unstructured Human Activity Detection from RGBD Images

Being able to detect and recognize human activities is essential for several applications, including personal assistive robotics. In this paper, we perform detection and recognition of unstructured human activity in unstructured environments. We use a RGBD sensor (Microsoft Kinect) as the input sensor, and compute a set of features based on human pose and motion, as well as based on image and pointcloud information. Our algorithm is based on a hierarchical maximum entropy Markov model (MEMM), which considers a person's activity as composed of a set of sub-activities. We infer the two-layered graph structure using a dynamic programming approach. We test our algorithm on detecting and recognizing twelve different activities performed by four people in different environments, such as a kitchen, a living room, an office, etc., and achieve good performance even when the person was not seen before in the training set.

cs.RO↗

arXiv2007

Structure and Problem Hardness: Goal Asymmetry and DPLL Proofs in SAT-Based Planning

In Verification and in (optimal) AI Planning, a successful method is to formulate the application as boolean satisfiability (SAT), and solve it with state-of-the-art DPLL-based procedures. There is a lack of understanding of why this works so well. Focussing on the Planning context, we identify a form of problem structure concerned with the symmetrical or asymmetrical nature of the cost of achieving the individual planning goals. We quantify this sort of structure with a simple numeric parameter called AsymRatio, ranging between 0 and 1. We run experiments in 10 benchmark domains from the International Planning Competitions since 2000; we show that AsymRatio is a good indicator of SAT solver performance in 8 of these domains. We then examine carefully crafted synthetic planning domains that allow control of the amount of structure, and that are clean enough for a rigorous analysis of the combinatorial search space. The domains are parameterized by size, and by the amount of structure. The CNFs we examine are unsatisfiable, encoding one planning step less than the length of the optimal plan. We prove upper and lower bounds on the size of the best possible DPLL refutations, under different settings of the amount of structure, as a function of size. We also identify the best possible sets of branching variables (backdoors). With minimum AsymRatio, we prove exponential lower bounds, and identify minimal backdoors of size linear in the number of variables. With maximum AsymRatio, we identify logarithmic DPLL refutations (and backdoors), showing a doubly exponential gap between the two structural extreme cases. The reasons for this behavior -- the proof arguments -- illuminate the prototypical patterns of structure causing the empirical behavior observed in the competition benchmarks.

cs.AI↗