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This work attempts to interpret modern deep (convolutional) networks from the principles of rate reduction and (shift) invariant classification. We show that the basic iterative gradient ascent scheme for optimizing the rate reduction of…

Modeling and predicting the dynamics of complex multiscale systems remains a significant challenge due to their inherent nonlinearities and sensitivity to initial conditions, as well as limitations of traditional machine learning methods…

We present a distributed anytime algorithm for performing MAP inference in graphical models. The problem is formulated as a linear programming relaxation over the edges of a graph. The resulting program has a constraint structure that…

During the past two decades, multi-agent optimization problems have drawn increased attention from the research community. When multiple objective functions are present among agents, many works optimize the sum of these objective functions.…

Multiobjective optimization plays an increasingly important role in modern applications, where several objectives are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to…

Higher-order data with high dimensionality is of immense importance in many areas of machine learning, computer vision, and video analytics. Multidimensional arrays (commonly referred to as tensors) are used for arranging higher-order data…

In the context of machine learning, disparate impact refers to a form of systematic discrimination whereby the output distribution of a model depends on the value of a sensitive attribute (e.g., race or gender). In this paper, we propose an…

Constructing complex computation from simpler building blocks is a defining problem of computer science. In algebraic automata theory, we represent computing devices as semigroups. Accordingly, we use mathematical tools like products and…

This paper extends the matrix based approach to the setting of multiple subdivision schemes studied in [Sauer 2012]. Multiple subdivision schemes, in contrast to stationary and non-stationary schemes, allow for level dependent subdivision…

Matrix factorization is an inference problem that has acquired importance due to its vast range of applications that go from dictionary learning to recommendation systems and machine learning with deep networks. The study of its fundamental…

Factorization machines and polynomial networks are supervised polynomial models based on an efficient low-rank decomposition. We extend these models to the multi-output setting, i.e., for learning vector-valued functions, with application…

Decomposing a deep neural network's learned representations into interpretable features could greatly enhance its safety and reliability. To better understand features, we adopt a geometric perspective, viewing them as a learned coordinate…

Many machine learning applications such as in vision, biology and social networking deal with data in high dimensions. Feature selection is typically employed to select a subset of features which im- proves generalization accuracy as well…

The widespread use of multisensor technology and the emergence of big datasets have created the need to develop tools to reduce, approximate, and classify large and multimodal data such as higher-order tensors. While early approaches…

Data splitting divides data into two parts. One part is reserved for model selection. In some applications, the second part is used for model validation but we use this part for estimating the parameters of the chosen model. We focus on the…

We present a palette-based framework for color composition for visual applications. Color composition is a critical aspect of visual applications in art, design, and visualization. The color wheel is often used to explain pleasing color…

In this paper we study scalar multivariate subdivision schemes with general integer expanding dilation matrix. Our main result yields simple algebraic conditions on the symbols of such schemes that characterize their polynomial…

Differential measurements of particle collisions or decays can provide stringent constraints on physics beyond the Standard Model of particle physics. In particular, the distributions of the kinematical and angular variables that…

We consider the problem of multi-task learning in the high dimensional setting. In particular, we introduce an estimator and investigate its statistical and computational properties for the problem of multiple connected linear regressions…

Multi-focus color image fusion refers to integrating multiple partially focused color images to create a single all-in-focus color image. However, existing methods struggle with complex real-world scenarios due to limitations in handling…