Data association, the problem of reasoning over correspondence between targets and measurements, is a fundamental problem in tracking. This paper presents a graphical model formulation of data association and applies an approximate inference method, belief propagation (BP), to obtain estimates of marginal association probabilities. We prove that BP is guaranteed to converge, and bound the number of iterations necessary. Experiments reveal a favourable comparison to prior methods in terms of accuracy and computational complexity.

Model-based methods and deep neural networks have both been tremendously successful paradigms in machine learning. In model-based methods, problem domain knowledge can be built into the constraints of the model, typically at the expense of difficulties during inference. In contrast, deterministic deep neural networks are constructed in such a way that inference is straightforward, but their architectures are generic and it is unclear how to incorporate knowledge. This work aims to obtain the advantages of both approaches. To do so, we start with a model-based approach and an associated inference algorithm, and \emph{unfold} the inference iterations as layers in a deep network. Rather than optimizing the original model, we \emph{untie} the model parameters across layers, in order to create a more powerful network. The resulting architecture can be trained discriminatively to perform accurate inference within a fixed network size. We show how this framework allows us to interpret conventional networks as mean-field inference in Markov random fields, and to obtain new architectures by instead using belief propagation as the inference algorithm. We then show its application to a non-negative matrix factorization model that incorporates the problem-domain knowledge that sound sources are additive. Deep unfolding of this model yields a new kind of non-negative deep neural network, that can be trained using a multiplicative backpropagation-style update algorithm. We present speech enhancement experiments showing that our approach is competitive with conventional neural networks despite using far fewer parameters.

Hyperspectral remote sensing images (HSIs) usually have high spectral resolution and low spatial resolution. Conversely, multispectral images (MSIs) usually have low spectral and high spatial resolutions. The problem of inferring images which combine the high spectral and high spatial resolutions of HSIs and MSIs, respectively, is a data fusion problem that has been the focus of recent active research due to the increasing availability of HSIs and MSIs retrieved from the same geographical area. We formulate this problem as the minimization of a convex objective function containing two quadratic data-fitting terms and an edge-preserving regularizer. The data-fitting terms account for blur, different resolutions, and additive noise. The regularizer, a form of vector Total Variation, promotes piecewise-smooth solutions with discontinuities aligned across the hyperspectral bands. The downsampling operator accounting for the different spatial resolutions, the non-quadratic and non-smooth nature of the regularizer, and the very large size of the HSI to be estimated lead to a hard optimization problem. We deal with these difficulties by exploiting the fact that HSIs generally "live" in a low-dimensional subspace and by tailoring the Split Augmented Lagrangian Shrinkage Algorithm (SALSA), which is an instance of the Alternating Direction Method of Multipliers (ADMM), to this optimization problem, by means of a convenient variable splitting. The spatial blur and the spectral linear operators linked, respectively, with the HSI and MSI acquisition processes are also estimated, and we obtain an effective algorithm that outperforms the state-of-the-art, as illustrated in a series of experiments with simulated and real-life data.

Interactions among people or objects are often dynamic in nature and can be represented as a sequence of networks, each providing a snapshot of the interactions over a brief period of time. An important task in analyzing such evolving networks is change-point detection, in which we both identify the times at which the large-scale pattern of interactions changes fundamentally and quantify how large and what kind of change occurred. Here, we formalize for the first time the network change-point detection problem within an online probabilistic learning framework and introduce a method that can reliably solve it. This method combines a generalized hierarchical random graph model with a Bayesian hypothesis test to quantitatively determine if, when, and precisely how a change point has occurred. We analyze the detectability of our method using synthetic data with known change points of different types and magnitudes, and show that this method is more accurate than several previously used alternatives. Applied to two high-resolution evolving social networks, this method identifies a sequence of change points that align with known external "shocks" to these networks.

We propose a Bayesian nonparametric approach to the problem of jointly modeling multiple related time series. Our model discovers a latent set of dynamical behaviors shared among the sequences, and segments each time series into regions defined by a subset of these behaviors. Using a beta process prior, the size of the behavior set and the sharing pattern are both inferred from data. We develop Markov chain Monte Carlo (MCMC) methods based on the Indian buffet process representation of the predictive distribution of the beta process. Our MCMC inference algorithm efficiently adds and removes behaviors via novel split-merge moves as well as data-driven birth and death proposals, avoiding the need to consider a truncated model. We demonstrate promising results on unsupervised segmentation of human motion capture data.

Machine learning methods are applied to finding the Green's function of the Anderson impurity model, a basic model system of quantum many-body condensed-matter physics. Different methods of parametrizing the Green's function are investigated; a representation in terms of Legendre polynomials is found to be superior due to its limited number of coefficients and its applicability to state of the art methods of solution. The dependence of the errors on the size of the training set is determined. The results indicate that a machine learning approach to dynamical mean-field theory may be feasible.

Noname manuscript No. (will be inserted by the editor) Abstract In this paper we present a greedy algorithm for solving the problem of the maximum partitioning of graphs with supply and demand (MPGSD). The goal of the method is to solve the MPGSD for large graphs in a reasonable time limit. This is done by using a two stage greedy algorithm, with two corresponding types of heuristics. The solutions acquired in this way are improved by applying a computationally inexpensive, hill climbing like, greedy correction procedure. In our numeric experiments we analyze different heuristic functions for each stage of the greedy algorithm, and show that their performance is highly dependent on the properties of the specific instance. Our tests show that by exploring a relatively small number of solutions generated by combining different heuristic functions, and applying the proposed correction procedure we can find solutions within only a few percent of the optimal ones. Keywords Graph Partitioning · Greedy Algorithm · Demand vertex · Supply vertex 1 Introduction A wide range of practical problems can be efficiently represented by means of graph partitioning. Present address: Qatar Environment and Energy Research Institute (QEERI), PO Box 5825, Doha, Qatar Abdelkader Bousselham Qatar Environment and Energy Research Institute (QEERI), PO Box 5825, Doha, Qatar Email: abousselham@qf.org.qa In this paper the focus is on the problem of maximum partitioning of a graph with supply and demand (MPGSD). This problem is defined on a graph G, in which each node is either a supply or a demand node. Each vertex v has a corresponding positive number, which is called the supply of node v; otherwise, if v is a demand node, this value would be called demand.

This paper proposes the use of the Brownian distance correlation to conduct a lead-lag analysis of financial and economic time series. When this methodology is applied to asset prices, the non-linear relationships identified may improve the price discovery process of these assets. The Brownian distance correlation determines relationships similar to those identified by the linear Granger causality test, and it also uncovers additional non-linear relationships among the log prices of oil, coal, and natural gas.

In this paper we present a novel agent-based modeling methodology to predict rooftop solar adoptions in the residential energy market. We first applied several linear regression models to estimate missing variables for non-adopters, so that attributes of non-adopters and adopters could be used to train a logistic regression model. Then, we integrated the logistic regression model along with other predictive models into a multi-agent simulation platform and validated our models by comparing the forecast of aggregate adoptions in a typical zip code area with its ground truth. This result shows that the agent-based model can reliably predict future adoptions. Finally, based on the validated agent-based model, we compared the outcome of a hypothesized seeding policy with the original incentive plan, and investigated other alternative seeding policies which could lead to more adopters.

The tight long-run fit of the learning curve has led to its use as a tool to predict the future cost of solar panels. Nemet (2006) is skeptical of the view that learning has been an important driver of cost reduction, and uses data during 1975-2002 to show that increases in plant size has been the most important driver of reduction in cost per watt.