Identifying important components or factors in large amounts of noisy data is a key problem in machine learning and data mining. Motivated by a pattern decomposition problem in materials discovery, aimed at discovering new materials for renewable energy, e.g. for fuel and solar cells, we introduce CombiFD, a framework for factor based pattern decomposition that allows the incorporation of a-priori knowledge as constraints, including complex combinatorial constraints. In addition, we propose a new pattern decomposition algorithm, called AMIQO, based on solving a sequence of (mixed-integer) quadratic programs. Our approach considerably outperforms the state of the art on the materials discovery problem, scaling to larger datasets and recovering more precise and physically meaningful decompositions. We also show the effectiveness of our approach for enforcing background knowledge on other application domains.

We propose a new algorithm called PLUTO for building logistic regression trees to binary response data. PLUTO can capture the nonlinear and interaction patterns in messy data by recursively partitioning the sample space. It fits a simple or a multiple linear logistic regression model in each partition. PLUTO employs the cyclical coordinate descent method for estimation of multiple linear logistic regression models with elastic net penalties, which allows it to deal with high-dimensional data efficiently. The tree structure comprises a graphical description of the data. Together with the logistic regression models, it provides an accurate classifier as well as a piecewise smooth estimate of the probability of "success". PLUTO controls selection bias by: (1) separating split variable selection from split point selection; (2) applying an adjusted chi-squared test to find the split variable instead of exhaustive search. A bootstrap calibration technique is employed to further correct selection bias. Comparison on real datasets shows that on average, the multiple linear PLUTO models predict more accurately than other algorithms.

We propose the product-of-filters (PoF) model, a generative model that decomposes audio spectra as sparse linear combinations of "filters" in the log-spectral domain. PoF makes similar assumptions to those used in the classic homomorphic filtering approach to signal processing, but replaces hand-designed decompositions built of basic signal processing operations with a learned decomposition based on statistical inference. This paper formulates the PoF model and derives a mean-field method for posterior inference and a variational EM algorithm to estimate the model's free parameters. We demonstrate PoF's potential for audio processing on a bandwidth expansion task, and show that PoF can serve as an effective unsupervised feature extractor for a speaker identification task.

We consider the problem of learning a set from random samples. We show how relevant geometric and topological properties of a set can be studied analytically using concepts from the theory of reproducing kernel Hilbert spaces. A new kind of reproducing kernel, that we call separating kernel, plays a crucial role in our study and is analyzed in detail. We prove a new analytic characterization of the support of a distribution, that naturally leads to a family of provably consistent regularized learning algorithms and we discuss the stability of these methods with respect to random sampling. Numerical experiments show that the approach is competitive, and often better, than other state of the art techniques.

We explore the idea that authoring a piece of text is an act of maximizing one's expected utility. To make this idea concrete, we consider the societally important decisions of the Supreme Court of the United States. Extensive past work in quantitative political science provides a framework for empirically modeling the decisions of justices and how they relate to text. We incorporate into such a model texts authored by amici curiae ("friends of the court" separate from the litigants) who seek to weigh in on the decision, then explicitly model their goals in a random utility model. We demonstrate the benefits of this approach in improved vote prediction and the ability to perform counterfactual analysis.

This dissertation shows that careful injection of noise into sample data can substantially speed up Expectation-Maximization algorithms. Expectation-Maximization algorithms are a class of iterative algorithms for extracting maximum likelihood estimates from corrupted or incomplete data. The convergence speed-up is an example of a noise benefit or "stochastic resonance" in statistical signal processing. The dissertation presents derivations of sufficient conditions for such noise-benefits and demonstrates the speed-up in some ubiquitous signal-processing algorithms. These algorithms include parameter estimation for mixture models, the $k$-means clustering algorithm, the Baum-Welch algorithm for training hidden Markov models, and backpropagation for training feedforward artificial neural networks. This dissertation also analyses the effects of data and model corruption on the more general Bayesian inference estimation framework. The main finding is a theorem guaranteeing that uniform approximators for Bayesian model functions produce uniform approximators for the posterior pdf via Bayes theorem. This result also applies to hierarchical and multidimensional Bayesian models.

This paper establishes the consistency of a family of graph-cut-based algorithms for clustering of data clouds. We consider point clouds obtained as samples of a ground-truth measure. We investigate approaches to clustering based on minimizing objective functionals defined on proximity graphs of the given sample. Our focus is on functionals based on graph cuts like the Cheeger and ratio cuts. We show that minimizers of the these cuts converge as the sample size increases to a minimizer of a corresponding continuum cut (which partitions the ground truth measure). Moreover, we obtain sharp conditions on how the connectivity radius can be scaled with respect to the number of sample points for the consistency to hold. We provide results for two-way and for multiway cuts. Furthermore we provide numerical experiments that illustrate the results and explore the optimality of scaling in dimension two.

Ensemble-of-trees methods have become popular choices for forecasting in both regression and classification problems. Algorithms such as random forests (Breiman 2001) and stochastic gradient boosting (Friedman 2002) are two well-established and widely employed procedures. Recent advances in ensemble methods include dynamic trees (Taddy, Gramacy, and Polson 2011) and Bayesian additive regression trees (BART, Chipman, George, and McCulloch 2010), which depart from predecessors in that they rely on an underlying Bayesian probability model rather than a pure algorithm. BART has demonstrated substantial promise in a wide variety of simulations and real world applications such as predicting avalanches on mountain roads (Blattenberger and Fowles 2014), predicting how transcription factors interact with DNA (Zhou and Liu 2008) and predicting movie box office revenues (Eliashberg 2010). This paper introduces bartMachine, a new R (R Core Team 2014) package available from the Comprehensive R Archive Network at http://CRAN.R-project.org/package

In this report paper we first present a report of the Advanced Machine Learning Course Project on the provided data set and then present a novel heuristic algorithm for exact Bayesian network (BN) structure discovery that uses decomposable scoring functions. Our algorithm follows a different approach to solve the problem of BN structure discovery than the previously used methods such as Dynamic Programming (DP) and Branch and Bound to reduce the search space and find the global optima space for the problem. The algorithm we propose has some degree of flexibility that can make it more or less greedy. The more the algorithm is set to be greedy, the more the speed of the algorithm will be, and the less optimal the final structure. Our algorithm runs in a much less time than the previously known methods and guarantees to have an optimality of close to 99%.

Solving logistic regression with L1-regularization in distributed settings is an important problem. This problem arises when training dataset is very large and cannot fit the memory of a single machine. We present d-GLMNET, a new algorithm solving logistic regression with L1-regularization in the distributed settings. We empirically show that it is superior over distributed online learning via truncated gradient.