In previous work, we proposed a logic-based framework in which computation is the execution of actions in an attempt to make reactive rules of the form if antecedent then consequent true in a canonical model of a logic program determined by an initial state, sequence of events, and the resulting sequence of subsequent states. In this model-theoretic semantics, reactive rules are the driving force, and logic programs play only a supporting role. In the canonical model, states, actions and other events are represented with timestamps. But in the operational semantics, for the sake of efficiency, timestamps are omitted and only the current state is maintained. State transitions are performed reactively by executing actions to make the consequents of rules true whenever the antecedents become true. This operational semantics is sound, but incomplete. It cannot make reactive rules true by preventing their antecedents from becoming true, or by proactively making their consequents true before their antecedents become true. In this paper, we characterize the notion of reactive model, and prove that the operational semantics can generate all and only such models. In order to focus on the main issues, we omit the logic programming component of the framework.

This paper considers probabilistic estimation of a low-rank matrix from non-linear element-wise measurements of its elements. We derive the corresponding approximate message passing (AMP) algorithm and its state evolution. Relying on non-rigorous but standard assumptions motivated by statistical physics, we characterize the minimum mean squared error (MMSE) achievable information theoretically and with the AMP algorithm. Unlike in related problems of linear estimation, in the present setting the MMSE depends on the output channel only trough a single parameter - its Fisher information. We illustrate this striking finding by analysis of submatrix localization, and of detection of communities hidden in a dense stochastic block model. For this example we locate the computational and statistical boundaries that are not equal for rank larger than four.

The aim of this paper is to provide a new method for learning the relationships between data that have been obtained independently. Unlike existing methods like matching, the proposed technique does not require any contextual information, provided that the dependency between the variables of interest is monotone. It can therefore be easily combined with matching in order to exploit the advantages of both methods. This technique can be described as a mix between quantile matching, and deconvolution. We provide for it a theoretical and an empirical validation.

The spectral $k$-support norm enjoys good estimation properties in low rank matrix learning problems, empirically outperforming the trace norm. Its unit ball is the convex hull of rank $k$ matrices with unit Frobenius norm. In this paper we generalize the norm to the spectral $(k,p)$-support norm, whose additional parameter $p$ can be used to tailor the norm to the decay of the spectrum of the underlying model. We characterize the unit ball and we explicitly compute the norm. We further provide a conditional gradient method to solve regularization problems with the norm, and we derive an efficient algorithm to compute the Euclidean projection on the unit ball in the case $p=\infty$. In numerical experiments, we show that allowing $p$ to vary significantly improves performance over the spectral $k$-support norm on various matrix completion benchmarks, and better captures the spectral decay of the underlying model.

Motivation: Public and private repositories of experimental data are growing to sizes that require dedicated methods for finding relevant data. To improve on the state of the art of keyword searches from annotations, methods for content-based retrieval have been proposed. In the context of gene expression experiments, most methods retrieve gene expression profiles, requiring each experiment to be expressed as a single profile, typically of case vs. control. A more general, recently suggested alternative is to retrieve experiments whose models are good for modelling the query dataset. However, for very noisy and high-dimensional query data, this retrieval criterion turns out to be very noisy as well. Results: We propose doing retrieval using a denoised model of the query dataset, instead of the original noisy dataset itself. To this end, we introduce a general probabilistic framework, where each experiment is modelled separately and the retrieval is done by finding related models. For retrieval of gene expression experiments, we use a probabilistic model called product partition model, which induces a clustering of genes that show similar expression patterns across a number of samples. The suggested metric for retrieval using clusterings is the normalized information distance. Empirical results finally suggest that inference for the full probabilistic model can be approximated with good performance using computationally faster heuristic clustering approaches (e.g. $k$-means). The method is highly scalable and straightforward to apply to construct a general-purpose gene expression experiment retrieval method. Availability: The method can be implemented using standard clustering algorithms and normalized information distance, available in many statistical software packages.

In this work, we introduce a novel class of adaptive Monte Carlo methods, called adaptive independent sticky MCMC algorithms, for efficient sampling from a generic target probability density function (pdf). The new class of algorithms employs adaptive non-parametric proposal densities which become closer and closer to the target as the number of iterations increases. The proposal pdf is built using interpolation procedures based on a set of support points which is constructed iteratively based on previously drawn samples. The algorithm's efficiency is ensured by a test that controls the evolution of the set of support points. This extra stage controls the computational cost and the convergence of the proposal density to the target. Each part of the novel family of algorithms is discussed and several examples are provided. Although the novel algorithms are presented for univariate target densities, we show that they can be easily extended to the multivariate context within a Gibbs-type sampler. The ergodicity is ensured and discussed. Exhaustive numerical examples illustrate the efficiency of sticky schemes, both as a stand-alone methods to sample from complicated one-dimensional pdfs and within Gibbs in order to draw from multi-dimensional target distributions.

Our paper deals with inferring simulator-based statistical models given some observed data. A simulator-based model is a parametrized mechanism which specifies how data are generated. It is thus also referred to as generative model. We assume that only a finite number of parameters are of interest and allow the generative process to be very general; it may be a noisy nonlinear dynamical system with an unrestricted number of hidden variables. This weak assumption is useful for devising realistic models but it renders statistical inference very difficult. The main challenge is the intractability of the likelihood function. Several likelihood-free inference methods have been proposed which share the basic idea of identifying the parameters by finding values for which the discrepancy between simulated and observed data is small. A major obstacle to using these methods is their computational cost. The cost is largely due to the need to repeatedly simulate data sets and the lack of knowledge about how the parameters affect the discrepancy. We propose a strategy which combines probabilistic modeling of the discrepancy with optimization to facilitate likelihood-free inference. The strategy is implemented using Bayesian optimization and is shown to accelerate the inference through a reduction in the number of required simulations by several orders of magnitude.

We propose a robust portfolio optimization approach based on quantile statistics. The proposed method is robust to extreme events in asset returns, and accommodates large portfolios under limited historical data. Specifically, we show that the risk of the estimated portfolio converges to the oracle optimal risk with parametric rate under weakly dependent asset returns. The theory does not rely on higher order moment assumptions, thus allowing for heavy-tailed asset returns. Moreover, the rate of convergence quantifies that the size of the portfolio under management is allowed to scale exponentially with the sample size of the historical data. The empirical effectiveness of the proposed method is demonstrated under both synthetic and real stock data. Our work extends existing ones by achieving robustness in high dimensions, and by allowing serial dependence.

We study the restless bandit problem where arms are associated with stationary $\varphi$-mixing processes and where rewards are therefore dependent: the question that arises from this setting is that of carefully recovering some independence by `ignoring' the values of some rewards. As we shall see, the bandit problem we tackle requires us to address the exploration/exploitation/independence trade-off, which we do by considering the idea of a {\em waiting arm} in the new Remix-UCB algorithm, a generalization of Improved-UCB for the problem at hand, that we introduce. We provide a regret analysis for this bandit strategy; two noticeable features of Remix-UCB are that i) it reduces to the regular Improved-UCB when the $\varphi$-mixing coefficients are all $0$, i.e. when the i.i.d scenario is recovered, and ii) when $\varphi(n)=O(n^{-\alpha})$, it is able to ensure a controlled regret of order $\Ot\left( \Delta_*^{(\alpha- 2)/\alpha} \log^{1/\alpha} T\right),$ where $\Delta_*$ encodes the distance between the best arm and the best suboptimal arm, even in the case when $\alpha<1$, i.e. the case when the $\varphi$-mixing coefficients {\em are not} summable.

This page includes forthcoming AAAI sponsored conferences, conferences presented by AAAI Affiliates, and conferences held in cooperation with AAAI. AI Magazine also maintains a calendar listing that includes nonaffiliated conferences at www.aaai.org/Magazine/calendar.php. AAAI-16 will be held Principles of Knowledge Representation on Semantic Computing. ICSC will February 12-17, 2016 in Phoenix, Arizona and Reasoning (KR 2016) be held February 3-5, 2016, in Laguna USA. Twenty-Ninth International Florida on Biomedical Engineering Systems IAAI-16 will be held will be AI Research Society Conference. and Technologies.