We introduce Church, a universal language for describing stochastic generative processes. Church is based on the Lisp model of lambda calculus, containing a pure Lisp as its deterministic subset. The semantics of Church is defined in terms of evaluation histories and conditional distributions on such histories. Church also includes a novel language construct, the stochastic memoizer, which enables simple description of many complex non-parametric models. We illustrate language features through several examples, including: a generalized Bayes net in which parameters cluster over trials, infinite PCFGs, planning by inference, and various non-parametric clustering models. Finally, we show how to implement query on any Church program, exactly and approximately, using Monte Carlo techniques.

Inference in large scale graphical models is an important task in many domains, and in particular probabilistic relational models (e.g. Markov logic networks). Such models often exhibit considerable symmetry, and it is a challenge to devise algorithms that exploit this symmetry to speed up inference. Recently, the automorphism group has been proposed to formalize mathematically what "exploiting symmetry" means. However, obtaining symmetry derived from automorphism is GI-hard, and consequently only a small fraction of the symmetry is easily available for effective employment. In this paper, we improve upon efficiency in two ways. First, we introduce the Cluster Signature Graph (CSG), a platform on which greater portions of the symmetries can be revealed and exploited. CSGs classify clusters of variables by projecting relations between cluster members onto a graph, allowing for the efficient pruning of symmetrical clusters even before their generation. Second, we introduce a novel framework based on CSGs for the Sherali-Adams hierarchy of linear program (LP) relaxations, dedicated to exploiting this symmetry for the benefit of tight Maximum A Posteriori (MAP) approximations. Combined with the pruning power of CSG, the framework quickly generates compact formulations for otherwise intractable LPs, as demonstrated by several empirical results.

Markov processes are widely used to generate sequences that imitate a given style, using random walk. Random walk generates sequences by iteratively concatenating states to prefixes of length equal or less than the given Markov order}. However, at higher orders, Markov chains tend to replicate chunks of the corpus with a size possibly higher than the order, a primary form of plagiarism. The Markov order defines a maximum length for training but not for generation. In the framework of constraint satisfaction (CSP), we introduce MaxOrder. This global constraint ensures that generated sequences do not include chunks larger than a given maximum order. We exhibit an automaton that recognises the solution set, with a size linear in the size of the corpus. We propose a linear-time procedure to generate this automaton from a corpus and a given max order. We then use this automaton to achieve generalised arc consistency for the MaxOrder constraint, holding on a sequence of size n, in O(n.T) time, where T is the size of the automaton. We illustrate our approach by generating text sequences from text corpora with a maximum order guarantee, effectively controlling plagiarism.

This paper will demonstrate a machine learning appli- cation for predicting positive lead conversion events on the Edmunds.com website, an American destination for car shopping. A positive conversion event occurs when a user fills out and submits a lead form interstitial. We used machine learning to identify which users might want to fill out lead forms, and where in their sessions to present the interstitials. There are several factors that make these predictions difficult, such as (a) far more negative than positive responses (b) seasonality effects due to car sales events near holidays, which require the model to be easily tunable and (c) the need for compu- tationally fast predictions for real-time decision-making in order to minimize any impact on the website’s us- ability. Rather than develop a single highly complex model, we used an ensemble of three simple models: Naive Bayes, Markov Chain, and Vowpal Wabbit. The ensemble generated significant lift over random predic- tions and demonstrated comparable accuracy to an ex- ternal consulting company’s model.

Conformant probabilistic planning (CPP) differs from conformant planning (CP) by two key elements: the initial belief state is probabilistic,and the conformant plan must achieve the goal with probability $\geq\theta$, for some $0<\theta\leq 1$. In earlier work we observed that one can reduce CPP to CP by finding a set of initial states whose probability $\geq\theta$, for whicha conformant plan exists. In previous solvers we used the underlying planner to select this set of states and to plan for them simultaneously. Here we suggest an alternative approach: start with relevance analysis to determine a promising set of initial states on which to focus. Then, call an off-the-shelf conformant planner to solve the resulting problem. This approach has a number of advantages. First, instead of depending on the heuristic function to select the set of initial states,we can introduce specific, efficient relevance reasoning techniques. Second, we can benefit from optimizations used by conformant planners that are unsound when applied to the original CPP. Finally, we are free to use any existing (or new) CP solver. Consequently, the new planner dominates previous solvers on almost all domains and scales to instances that were not solved before.

Many real-world applications involve multilabel classification, in which the labels can have strong inter-dependencies and some of them may even be missing.Existing multilabel algorithms are unable to handle both issues simultaneously.In this paper, we propose a probabilistic model that can automatically learn and exploit multilabel correlations.By integrating out the missing information, it also provides a disciplinedapproach to the handling of missing labels. The inference procedure is simple, and the optimization subproblems are convex. Experiments on a number of real-world data sets with both complete and missing labelsdemonstrate that the proposed algorithm can consistently outperform state-of-the-art multilabel classification algorithms.

In machine learning and statistics, probabilistic inference involving multimodal distributions is quite difficult. This is especially true in high dimensional problems, where most existing algorithms cannot easily move from one mode to another. To address this issue, we propose a novel Bayesian inference approach based on Markov Chain Monte Carlo. Our method can effectively sample from multimodal distributions, especially when the dimension is high and the modes are isolated. To this end, it exploits and modifies the Riemannian geometric properties of the target distribution to create \emph{wormholes} connecting modes in order to facilitate moving between them. Further, our proposed method uses the regeneration technique in order to adapt the algorithm by identifying new modes and updating the network of wormholes without affecting the stationary distribution. To find new modes, as opposed to rediscovering those previously identified, we employ a novel mode searching algorithm that explores a \emph{residual energy} function obtained by subtracting an approximate Gaussian mixture density (based on previously discovered modes) from the target density function.

Central to robot exploration and mapping is the task of persistent localization in environmental fields characterized by spatially correlated measurements. This paper presents a Gaussian process localization (GP-Localize) algorithm that, in contrast to existing works, can exploit the spatially correlated field measurements taken during a robot's exploration (instead of relying on prior training data) for efficiently and scalably learning the GP observation model online through our proposed novel online sparse GP. As a result, GP-Localize is capable of achieving constant time and memory (i.e., independent of the size of the data) per filtering step, which demonstrates the practical feasibility of using GPs for persistent robot localization and autonomy. Empirical evaluation via simulated experiments with real-world datasets and a real robot experiment shows that GP-Localize outperforms existing GP localization algorithms.

A recent breadth-first branch and bound algorithm (BFBnB)for learning Bayesian network structures (Maloneet al. 2011) uses two bounds to prune the searchspace for better efficiency; one is a lower bound calculatedfrom pattern database heuristics, and the otheris an upper bound obtained by a hill climbing search.Whenever the lower bound of a search path exceeds theupper bound, the path is guaranteed to lead to suboptimalsolutions and is discarded immediately. This paperintroduces methods for tightening the bounds. Thelower bound is tightened by using more informed variablegroupings when creating the pattern databases, andthe upper bound is tightened using an anytime learningalgorithm. Empirical results show that these boundsimprove the efficiency of Bayesian network learning bytwo to three orders of magnitude.

In many probabilistic planning scenarios, a system’s behavior needs to not only maximize the expected utility but also obey certain restrictions. This paper presents Saturated Path-Constrained Markov Decision Processes (SPC MDPs), a new MDP type for planning under uncertainty with deterministic model-checking constraints, e.g., "state s must be visited befores s'", "the system must end up in s", or "the system must never enter s". We present a mathematical analysis of SPCMDPs, showing that although SPC MDPs generally have no optimal policies, every instance of this class has an epsilon-optimal randomized policy for any > 0. We propose a dynamic programming-based algorithm for finding such policies, and empirically demonstrate this algorithm to be orders of magnitude faster than its next-best alternative.