In many personalised recommendation problems, there are examples of items users prefer or like, but no examples of items they dislike. A state-of-the-art method for such implicit feedback, or one-class collaborative filtering (OC-CF), problems is SLIM, which makes recommendations based on a learned item-item similarity matrix. While SLIM has been shown to perform well on implicit feedback tasks, we argue that it is hindered by two limitations: first, it does not produce user-personalised predictions, which hampers recommendation performance; second, it involves solving a constrained optimisation problem, which impedes fast training. In this paper, we propose LRec, a variant of SLIM that overcomes these limitations without sacrificing any of SLIM's strengths.At its core, LRec employs linear logistic regression; despite this simplicity, LRec consistently and significantly outperforms all existing methods on a range of datasets. Our results thus illustrate that the OC-CF problem can be effectively tackled via linear classification models.

Probabilistic inference in many real-world problems requires graphical models with deterministic algebraic constraints between random variables (e.g., Newtonian mechanics, Pascal’s law, Ohm’s law) that are known to be problematic for many inference methods such as Monte Carlo sampling. Fortunately, when such constraintsare invertible, the model can be collapsed and the constraints eliminated through the well-known Jacobian-based change of variables. As our first contributionin this work, we show that a much broader classof algebraic constraints can be collapsed by leveraging the properties of a Dirac delta model of deterministic constraints. Unfortunately, the collapsing processcan lead to highly piecewise densities that pose challenges for existing probabilistic inference tools. Thus,our second contribution to address these challenges is to present a variation of Gibbs sampling that efficiently samples from these piecewise densities. The key insight to achieve this is to introduce a class of functions that (1) is sufficiently rich to approximate arbitrary models up to arbitrary precision, (2) is closed under dimension reduction (collapsing) for models with (non)linear algebraic constraints and (3) always permits one analytical integral sufficient to automatically derive closed-form conditionals for Gibbs sampling. Experiments demonstrate the proposed sampler converges at least an order of magnitude faster than existing Monte Carlo samplers.

We review the 2014 International Planning Competition (IPC-2014), the eighth in a series of competitions starting in 1998. IPC-2014 was held in three separate parts to assess state-of-the-art in three prominent areas of planning research: the deterministic (classical) part (IPCD), the learning part (IPCL), and the probabilistic part (IPPC). Each part evaluated planning systems in ways that pushed the edge of existing planner performance by introducing new challenges, novel tasks, or both. The competition surpassed again the number of competitors than its predecessor, highlighting the competition’s central role in shaping the landscape of ongoing developments in evaluating planning systems.

Recent advances in Symbolic Dynamic Programming (SDP) combined withthe extended algebraic decision diagram (XADD) have provided exactsolutions for expressive subclasses of finite-horizon Hybrid MarkovDecision Processes (HMDPs) with mixed continuous and discrete stateand action parameters. Unfortunately, SDP suffers from two majordrawbacks: (1) it solves for all states and can be intractable formany problems that inherently have large optimal XADD value functionrepresentations; and (2) it cannot maintain compact (pruned) XADDrepresentations for domains with nonlinear dynamics and reward due tothe need for nonlinear constraint checking. In this work, wesimultaneously address both of these problems by introducing real-timeSDP (RTSDP). RTSDP addresses (1) by focusing the solution and valuerepresentation only on regions reachable from a set of initial statesand RTSDP addresses (2) by using visited states as witnesses ofreachable regions to assist in pruning irrelevant or unreachable(nonlinear) regions of the value function. To this end, RTSDP enjoysprovable convergence over the set of initial states and substantialspace and time savings over SDP as we demonstrate in a variety of hybrid domains ranging from inventory to reservoir to traffic control.

Bayesian decision-theory underpins robust decision-making in applications ranging from plant control to robotics where hedging action selection against state uncertainty is critical for minimizing low probability but potentially catastrophic outcomes (e.g, uncontrollable plant conditions or robots falling into stairwells). Unfortunately, belief state distributions in such settings are often complex and/or high dimensional, thus prohibiting the efficient application of analytical techniques for expected utility computation when real-time control is required. This leaves Monte Carlo evaluation as one of the few viable (and hence frequently used) techniques for online action selection. However, loss-insensitive Monte Carlo methods may require large numbers of samples to identify optimal actions with high certainty since they may sample from highprobability regions that do not disambiguate action utilities. In this paper we remedy this problem by deriving an optimal proposal distribution for a loss-calibrated Monte Carlo importance sampler that bounds the regret of using an estimated optimal action. Empirically, we show that using our loss-calibrated Monte Carlo method yields high-accuracy optimal action selections in a fraction of the number of samples required by conventional loss-insensitive samplers.

Naive Bayes (NB) is well-known to be a simple but effective classifier, especially when combined with feature selection. Unfortunately, feature selection methods are often greedy and thus cannot guarantee an optimal feature set is selected. An alternative to feature selection is to use Bayesian model averaging (BMA), which computes a weighted average over multiple predictors; when the different predictor models correspond to different feature sets, BMA has the advantage over feature selection that its predictions tend to have lower variance on average in comparison to any single model. In this paper, we show for the first time that it is possible to exactly evaluate BMA over the exponentially-sized powerset of NB feature models in linear-time in the number of features; this yields an algorithm about as expensive to train as a single NB model with all features, but yet provably converges to the globally optimal feature subset in the asymptotic limit of data. We evaluate this novel BMA-NB classifier on a range of datasets showing that it never underperforms NB (as expected) and sometimes offers performance competitive (or superior) to classifiers such as SVMs and logistic regression while taking a fraction of the time to train.

Many real-world Bayesian inference problems such as preference learning or trader valuation modeling in financial markets naturally use piecewise likelihoods. Unfortunately, exact closed-form inference in the underlying Bayesian graphical models is intractable in the general case and existing approximation techniques provide few guarantees on both approximation quality and efficiency. While (Markov Chain) Monte Carlo methods provide an attractive asymptotically unbiased approximation approach, rejection sampling and Metropolis-Hastings both prove inefficient in practice, and analytical derivation of Gibbs samplers require exponential space and time in the amount of data. In this work, we show how to transform problematic piecewise likelihoods into equivalent mixture models and then provide a blocked Gibbs sampling approach for this transformed model that achieves an exponential-to-linear reduction in space and time compared to a conventional Gibbs sampler. This enables fast, asymptotically unbiased Bayesian inference in a new expressive class of piecewise graphical models and empirically requires orders of magnitude less time than rejection, Metropolis-Hastings, and conventional Gibbs sampling methods to achieve the same level of accuracy.

Partially-observable Markov decision processes (POMDPs) provide a powerful model for real-world sequential decision-making problems. In recent years, point- based value iteration methods have proven to be extremely effective techniques for finding (approximately) optimal dynamic programming solutions to POMDPs when an initial set of belief states is known. However, no point-based work has provided exact point-based backups for both continuous state and observation spaces, which we tackle in this paper. Our key insight is that while there may be an infinite number of possible observations, there are only a finite number of observation partitionings that are relevant for optimal decision-making when a finite, fixed set of reachable belief states is known. To this end, we make two important contributions: (1) we show how previous exact symbolic dynamic pro- gramming solutions for continuous state MDPs can be generalized to continu- ous state POMDPs with discrete observations, and (2) we show how this solution can be further extended via recently developed symbolic methods to continuous state and observations to derive the minimal relevant observation partitioning for potentially correlated, multivariate observation spaces. We demonstrate proof-of- concept results on uni- and multi-variate state and observation steam plant control.

Probabilistic reasoning in the real-world often requires inference incontinuous variable graphical models, yet there are few methods for exact, closed-form inference when joint distributions are non-Gaussian. To address this inferential deficit, we introduce SVE -- a symbolic extension of the well-known variable elimination algorithm to perform exact inference in an expressive class of mixed discrete and continuous variable graphical models whose conditional probability functions can be well-approximated as piecewise combinations of polynomials with bounded support. Using this representation, we show that we can compute all of the SVE operations exactly and in closed-form, which crucially includes definite integration w.r.t. multivariate piecewise polynomial functions. To aid in the efficient computation and compact representation of this solution, we use an extended algebraic decision diagram (XADD) data structure that supports all SVE operations. We provide illustrative results for SVE on probabilistic inference queries inspired by robotics localization and tracking applications that mix various continuous distributions; this represents the first time a general closed-form exact solution has been proposed for this expressive class of discrete/continuous graphical models.

Many real-world decision-theoretic planning problemsare naturally modeled using both continuous state andaction (CSA) spaces, yet little work has provided ex-act solutions for the case of continuous actions. Inthis work, we propose a symbolic dynamic program-ming (SDP) solution to obtain the optimal closed-formvalue function and policy for CSA-MDPs with mul-tivariate continuous state and actions, discrete noise,piecewise linear dynamics, and piecewise linear (or re-stricted piecewise quadratic) reward. Our key contribu-tion over previous SDP work is to show how the contin-uous action maximization step in the dynamic program-ming backup can be evaluated optimally and symboli-cally — a task which amounts to symbolic constrainedoptimization subject to unknown state parameters; wefurther integrate this technique to work with an efficientand compact data structure for SDP — the extendedalgebraic decision diagram (XADD). We demonstrateempirical results on a didactic nonlinear planning exam-ple and two domains from operations research to showthe first automated exact solution to these problems.