Coordinate descent methods employ random partial updates of decision variables in order to solve huge-scale convex optimization problems. In this work, we introduce new adaptive rules for the random selection of their updates. By adaptive, we mean that our selection rules are based on the dual residual or the primal-dual gap estimates and can change at each iteration. We theoretically characterize the performance of our selection rules and demonstrate improvements over the state-of-the-art, and extend our theory and algorithms to general convex objectives. Numerical evidence with hinge-loss support vector machines and Lasso confirm that the practice follows the theory.

We propose a novel coding theoretic framework for mitigating stragglers in distributed learning. We show how carefully replicating data blocks and coding across gradients can provide tolerance to failures and stragglers for Synchronous Gradient Descent. We implement our schemes in python (using MPI) to run on Amazon EC2, and show how we compare against baseline approaches in running time and generalization error.

Many objects in the real world are difficult to describe by a single numerical vector of a fixed length, whereas describing them by a set of vectors is more natural. Therefore, Multiple instance learning (MIL) techniques have been constantly gaining on importance throughout last years. MIL formalism represents each object (sample) by a set (bag) of feature vectors (instances) of fixed length where knowledge about objects (e.g., class label) is available on bag level but not necessarily on instance level. Many standard tools including supervised classifiers have been already adapted to MIL setting since the problem got formalized in late nineties. In this work we propose a neural network (NN) based formalism that intuitively bridges the gap between MIL problem definition and the vast existing knowledge-base of standard models and classifiers. We show that the proposed NN formalism is effectively optimizable by a modified back-propagation algorithm and can reveal unknown patterns inside bags. Comparison to eight types of classifiers from the prior art on a set of 14 publicly available benchmark datasets confirms the advantages and accuracy of the proposed solution.

Each year, roughly 30% of first-year students at US baccalaureate institutions do not return for their second year and over $9 billion is spent educating these students. Yet, little quantitative research has analyzed the causes and possible remedies for student attrition. Here, we describe initial efforts to model student dropout using the largest known dataset on higher education attrition, which tracks over 32,500 students' demographics and transcript records at one of the nation's largest public universities. Our results highlight several early indicators of student attrition and show that dropout can be accurately predicted even when predictions are based on a single term of academic transcript data. These results highlight the potential for machine learning to have an impact on student retention and success while pointing to several promising directions for future work.

Bayesian optimization has become a successful tool for hyperparameter optimization of machine learning algorithms, such as support vector machines or deep neural networks. Despite its success, for large datasets, training and validating a single configuration often takes hours, days, or even weeks, which limits the achievable performance. To accelerate hyperparameter optimization, we propose a generative model for the validation error as a function of training set size, which is learned during the optimization process and allows exploration of preliminary configurations on small subsets, by extrapolating to the full dataset. We construct a Bayesian optimization procedure, dubbed Fabolas, which models loss and training time as a function of dataset size and automatically trades off high information gain about the global optimum against computational cost. Experiments optimizing support vector machines and deep neural networks show that Fabolas often finds high-quality solutions 10 to 100 times faster than other state-of-the-art Bayesian optimization methods or the recently proposed bandit strategy Hyperband.

Clustering is an underspecified task: there are no universal criteria for what makes a good clustering. This is especially true for relational data, where similarity can be based on the features of individuals, the relationships between them, or a mix of both. Existing methods for relational clustering have strong and often implicit biases in this respect. In this paper, we introduce a novel similarity measure for relational data. It is the first measure to incorporate a wide variety of types of similarity, including similarity of attributes, similarity of relational context, and proximity in a hypergraph. We experimentally evaluate how using this similarity affects the quality of clustering on very different types of datasets. The experiments demonstrate that (a) using this similarity in standard clustering methods consistently gives good results, whereas other measures work well only on datasets that match their bias; and (b) on most datasets, the novel similarity outperforms even the best among the existing ones.

Machine learning is one of the fastest growing areas of computer science, with far-reaching applications. The aim of this textbook is to introduce machine learning, and the algorithmic paradigms it offers, in a principled way. The book provides an extensive theoretical account of the fundamental ideas underlying machine learning and the mathematical derivations that transform these principles into practical algorithms. Following a presentation of the basics of the field, the book covers a wide array of central topics that have not been addressed by previous textbooks. These include a discussion of the computational complexity of learning and the concepts of convexity and stability; important algorithmic paradigms including stochastic gradient descent, neural networks, and structured output learning; and emerging theoretical concepts such as the PAC-Bayes approach and compression-based bounds.

We discuss a Bayesian formulation to coarse-graining (CG) of PDEs where the coefficients (e.g. material parameters) exhibit random, fine scale variability. The direct solution to such problems requires grids that are small enough to resolve this fine scale variability which unavoidably requires the repeated solution of very large systems of algebraic equations. We establish a physically inspired, data-driven coarse-grained model which learns a low- dimensional set of microstructural features that are predictive of the fine-grained model (FG) response. Once learned, those features provide a sharp distribution over the coarse scale effec- tive coefficients of the PDE that are most suitable for prediction of the fine scale model output. This ultimately allows to replace the computationally expensive FG by a generative proba- bilistic model based on evaluating the much cheaper CG several times. Sparsity enforcing pri- ors further increase predictive efficiency and reveal microstructural features that are important in predicting the FG response. Moreover, the model yields probabilistic rather than single-point predictions, which enables the quantification of the unavoidable epistemic uncertainty that is present due to the information loss that occurs during the coarse-graining process.

In this paper we propose a synergistic melting of neural networks and decision trees (DT) we call neural decision trees (NDT). NDT is an architecture a la decision tree where each splitting node is an independent multilayer perceptron allowing oblique decision functions or arbritrary nonlinear decision function if more than one layer is used. This way, each MLP can be seen as a node of the tree. We then show that with the weight sharing asumption among those units, we end up with a Hashing Neural Network (HNN) which is a multilayer perceptron with sigmoid activation function for the last layer as opposed to the standard softmax. The output units then jointly represent the probability to be in a particular region. The proposed framework allows for global optimization as opposed to greedy in DT and differentiability w.r.t. all parameters and the input, allowing easy integration in any learnable pipeline, for example after CNNs for computer vision tasks. We also demonstrate the modeling power of HNN allowing to learn union of disjoint regions for final clustering or classification making it more general and powerful than standard softmax MLP requiring linear separability thus reducing the need on the inner layer to perform complex data transformations. We finally show experiments for supervised, semi-suppervised and unsupervised tasks and compare results with standard DTs and MLPs.

To improve the efficiency of Monte Carlo estimation, practitioners are turning to biased Markov chain Monte Carlo procedures that trade off asymptotic exactness for computational speed. The reasoning is sound: a reduction in variance due to more rapid sampling can outweigh the bias introduced. However, the inexactness creates new challenges for sampler and parameter selection, since standard measures of sample quality like effective sample size do not account for asymptotic bias. To address these challenges, we introduce a new computable quality measure based on Stein's method that quantifies the maximum discrepancy between sample and target expectations over a large class of test functions. We use our tool to compare exact, biased, and deterministic sample sequences and illustrate applications to hyperparameter selection, convergence rate assessment, and quantifying bias-variance tradeoffs in posterior inference.