We propose a novel method for maximum likelihood-based parameter inference in nonlinear and/or non-Gaussian state space models. The method is an iterative procedure with three steps. At each iteration a particle filter is used to estimate the value of the log-likelihood function at the current parameter iterate. Using these log-likelihood estimates, a surrogate objective function is created by utilizing a Gaussian process model. Finally, we use a heuristic procedure to obtain a revised parameter iterate, providing an automatic trade-off between exploration and exploitation of the surrogate model. The method is profiled on two state space models with good performance both considering accuracy and computational cost.

We present a general framework for accelerating a large class of widely used Markov chain Monte Carlo (MCMC) algorithms. Our approach exploits fast, iterative approximations to the target density to speculatively evaluate many potential future steps of the chain in parallel. The approach can accelerate computation of the target distribution of a Bayesian inference problem, without compromising exactness, by exploiting subsets of data. It takes advantage of whatever parallel resources are available, but produces results exactly equivalent to standard serial execution. In the initial burn-in phase of chain evaluation, it achieves speedup over serial evaluation that is close to linear in the number of available cores.

Emission from a class of benzene-based molecules known as Polycyclic Aromatic Hydrocarbons (PAHs) dominates the infrared spectrum of star-forming regions. The observed emission appears to arise from the combined emission of numerous PAH species, each with its unique spectrum. Linear superposition of the PAH spectra identifies this problem as a source separation problem. It is, however, of a formidable class of source separation problems given that different PAH sources potentially number in the hundreds, even thousands, and there is only one measured spectral signal for a given astrophysical site. Fortunately, the source spectra of the PAHs are known, but the signal is also contaminated by other spectral sources. We describe our ongoing work in developing Bayesian source separation techniques relying on nested sampling in conjunction with an ON/OFF mechanism enabling simultaneous estimation of the probability that a particular PAH species is present and its contribution to the spectrum.

Mach Learn manuscript No. (will be inserted by the editor) Abstract We present a new application and covering number bound for the framework of "Machine Learning with Operational Costs (MLOC)," which is an exploratory form of decision theory. The MLOC framework incorporates knowledge about how a predictive model will be used for a subsequent task, thus combining machine learning with the decision that is made afterwards. In this work, we use the MLOC framework to study a problem that has implications for power grid reliability and maintenance, called the Machine Learning and Traveling Repairman Problem (ML&TRP). The goal of the ML&TRP is to determine a route for a "repair crew," which repairs nodes on a graph. The repair crew aims to minimize the cost of failures at the nodes, but as in many real situations, the failure probabilities are not known and must be estimated. The MLOC framework allows us to understand how this uncertainty influences the repair route. Keywords decision theory · generalization bound · constrained linear function classes · covering numbers · traveling repairman · mixed-integer programming 1 Introduction In many domains, it is essential to understand how uncertainty in predictions influences decision-making. Funding for Theja Tulabandhula was provided by a Fulbright Fellowship and Xerox Fellowship. Cynthia Rudin's work on this project was funded in part by Con Edison, by the MIT Energy Initiative Seed Fund, and NSF grant IIS-1053407. The new framework of Machine Learning with Operational Costs (MLOC) (Tulabandhula and Rudin, 2013) provides a mechanism to do this, and is a type of exploratory decision theory. Where usual decision theories provide a single policy that minimizes expected costs, the MLOC framework is able to produce a range of reasonable policies that span the full set of reasonable costs. To do this, the operational cost becomes a regularization term within the machine learning model, and adjusting the regularization constant allows us to explore solutions for all reasonable costs. This gives decision makers a way to understand the uncertainty in their predictive model in terms of something they can grasp - uncertainty in the cost to solve the problem. The MLOC framework can also be used in another way, namely to incorporate prior knowledge about the cost to produce a better predictive model.

In this survey we present different approaches that allow an intelligent agent to explore autonomous its environment to gather information and learn multiple tasks. Different communities proposed different solutions, that are in many cases, similar and/or complementary. These solutions include active learning, exploration/exploitation, online-learning and social learning. The common aspect of all these approaches is that it is the agent to selects and decides what information to gather next. Applications for these approaches already include tutoring systems, autonomous grasping learning, navigation and mapping and human-robot interaction. We discuss how these approaches are related, explaining their similarities and their differences in terms of problem assumptions and metrics of success. We consider that such an integrated discussion will improve inter-disciplinary research and applications.

Abstract--This paper introduces a robust mixing model to describe hyperspectral data resulting from the mixture of several pure spectral signatures. This new model not only generalizes the commonly used linear mixing model, but also allows for possible nonlinear effects to be easily handled, relying on mild assumptions regarding these nonlinearities. The standard nonnegativity and sum-to-one constraints inherent to spectral unmixing are coupled with a group-sparse constraint imposed on the nonlinearity component. The data fidelity term is expressed as a β -divergence, a continuous family of dissimilarity measures that takes the squared Euclidean distance and the generalized Kullback-Leibler divergence as special cases. The penalized objective is minimized with a block-coordinate descent that involves majorization-minimization updates. Simulation results obtained on synthetic and real data show that the proposed strategy competes with state-of-the-art linear and nonlinear unmixing methods. Spectral unmixing (SU) is an issue of prime interest when analyzing hyperspectral data since it provides a comprehensive and meaningful description of the collected measurements in various application fields including remote sensing [1], planetology [2], food monitoring [3] or spectro-microscopy [4]. Most of the hyperspectral unmixing algorithms proposed in the signal & image processing and geoscience literatures rely on the commonly admitted linear mixing model (LMM),Y MA . Indeed, LMM provides a good approximation of the physical process underlying the observations and has resulted in interesting results for most applications. However, for several specific applications, LMM may be inaccurate and other nonlinear models need to be advocated [7]. For instance, in remotely sensed images composed of vegetation (e.g., trees), interactions of photons with multiple components of the scene lead to nonlinear effects that can be taken into account N. Dobigeon is with University of Toulouse, IRIT/INP-ENSEEIHT, 2 rue Camichel, BP 7122, 31071 Toulouse cedex 7, France.

Recent SVD-free matrix factorization formulations have enabled rank minimization for systems with millions of rows and columns, paving the way for matrix completion in extremely large-scale applications, such as seismic data interpolation. In this paper, we consider matrix completion formulations designed to hit a target data-fitting error level provided by the user, and propose an algorithm called LR-BPDN that is able to exploit factorized formulations to solve the corresponding optimization problem. Since practitioners typically have strong prior knowledge about target error level, this innovation makes it easy to apply the algorithm in practice, leaving only the factor rank to be determined. Within the established framework, we propose two extensions that are highly relevant to solving practical challenges of data interpolation. First, we propose a weighted extension that allows known subspace information to improve the results of matrix completion formulations. We show how this weighting can be used in the context of frequency continuation, an essential aspect to seismic data interpolation. Second, we propose matrix completion formulations that are robust to large measurement errors in the available data. We illustrate the advantages of LR-BPDN on the collaborative filtering problem using the MovieLens 1M, 10M, and Netflix 100M datasets. Then, we use the new method, along with its robust and subspace re-weighted extensions, to obtain high-quality reconstructions for large scale seismic interpolation problems with real data, even in the presence of data contamination.

The smart grid vision entails advanced information technology and data analytics to enhance the efficiency, sustainability, and economics of the power grid infrastructure. Aligned to this end, modern statistical learning tools are leveraged here for electricity market inference. Day-ahead price forecasting is cast as a low-rank kernel learning problem. Uniquely exploiting the market clearing process, congestion patterns are modeled as rank-one components in the matrix of spatio-temporally varying prices. Through a novel nuclear norm-based regularization, kernels across pricing nodes and hours can be systematically selected. Even though market-wide forecasting is beneficial from a learning perspective, it involves processing high-dimensional market data. The latter becomes possible after devising a block-coordinate descent algorithm for solving the non-convex optimization problem involved. The algorithm utilizes results from block-sparse vector recovery and is guaranteed to converge to a stationary point. Numerical tests on real data from the Midwest ISO (MISO) market corroborate the prediction accuracy, computational efficiency, and the interpretative merits of the developed approach over existing alternatives.

We describe an adaptation of the simulated annealing algorithm to nonparametric clustering and related probabilistic models. This new algorithm learns nonparametric latent structure over a growing and constantly churning subsample of training data, where the portion of data subsampled can be interpreted as the inverse temperature beta(t) in an annealing schedule. Gibbs sampling at high temperature (i.e., with a very small subsample) can more quickly explore sketches of the final latent state by (a) making longer jumps around latent space (as in block Gibbs) and (b) lowering energy barriers (as in simulated annealing). We prove subsample annealing speeds up mixing time N^2 -> N in a simple clustering model and exp(N) -> N in another class of models, where N is data size. Empirically subsample-annealing outperforms naive Gibbs sampling in accuracy-per-wallclock time, and can scale to larger datasets and deeper hierarchical models. We demonstrate improved inference on million-row subsamples of US Census data and network log data and a 307-row hospital rating dataset, using a Pitman-Yor generalization of the Cross Categorization model.

This paper presents an implementation of the Imperialist Competitive Algorithm (ICA) for solving the fuzzy random portfolio selection problem where the asset returns are represented by fuzzy random variables. Portfolio Optimization is an important research field in modern finance. By using the necessity-based model, fuzzy random variables reformulate to the linear programming and ICA will be designed to find the optimum solution. To show the efficiency of the proposed method, a numerical example illustrates the whole idea on implementation of ICA for fuzzy random portfolio selection problem.