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Decision Trees (DTs) are commonly used for many machine learning tasks due to their high degree of interpretability. However, learning a DT from data is a difficult optimization problem, as it is non-convex and non-differentiable.…

We develop new approximation algorithms and data structures for representing and computing with multivariate functions using the functional tensor-train (FT), a continuous extension of the tensor-train (TT) decomposition. The FT represents…

Low precision training can significantly reduce the computational overhead of training deep neural networks (DNNs). Though many such techniques exist, cyclic precision training (CPT), which dynamically adjusts precision throughout training…

Discrete trigonometric transforms (DTTs), such as the DCT-2 and the DST-7, are widely used in video codecs for their balance between coding performance and computational efficiency. In contrast, data-dependent transforms, such as the…

Low-Dose computer tomography (LDCT) is an ideal alternative to reduce radiation risk in clinical applications. Although supervised-deep-learning-based reconstruction methods have demonstrated superior performance compared to conventional…

This work analyzes the solution trajectory of gradient-based algorithms via a novel basis function decomposition. We show that, although solution trajectories of gradient-based algorithms may vary depending on the learning task, they behave…

Image segmentation is the foundation of several computer vision tasks, where pixel-wise knowledge is a prerequisite for achieving the desired target. Deep learning has shown promising performance in supervised image segmentation. However,…

Neural networks (NNs) can be viewed as approximation tools. Traditionally, NNs are relying on gradient and stochastic gradient (SG) methods. There are a number of available computational packages for constructing least squares…

Deep-learning density functional theory (DFT) shows great promise to significantly accelerate material discovery and potentially revolutionize materials research. However, current research in this field primarily relies on data-driven…

Coordinate descent (CD) algorithms have become the method of choice for solving a number of optimization problems in machine learning. They are particularly popular for training linear models, including linear support vector machine…

Knowledge tracing (KT) models are a popular approach for predicting students' future performance at practice problems using their prior attempts. Though many innovations have been made in KT, most models including the state-of-the-art Deep…

Despite their widespread success, the application of deep neural networks to functional data remains scarce today. The infinite dimensionality of functional data means standard learning algorithms can be applied only after appropriate…

This paper compares the performance of a NN taking the output of a DCT (Discrete Cosine Transform) of an image patch with leNet for classifying MNIST hand written digits. The basis functions underlying the DCT bear a passing resemblance to…

Learning approximations to smooth target functions of many variables from finite sets of pointwise samples is an important task in scientific computing and its many applications in computational science and engineering. Despite well over…

Using function approximation to represent a value function is necessary for continuous and high-dimensional state spaces. Linear function approximation has desirable theoretical guarantees and often requires less compute and samples than…

We propose a DC proximal Newton algorithm for solving nonconvex regularized sparse learning problems in high dimensions. Our proposed algorithm integrates the proximal Newton algorithm with multi-stage convex relaxation based on the…

Deep neural networks need a big amount of training data, while in the real world there is a scarcity of data available for training purposes. To resolve this issue unsupervised methods are used for training with limited data. In this…

The task of approximating an arbitrary convex function arises in several learning problems such as convex regression, learning with a difference of convex (DC) functions, and learning Bregman or $f$-divergences. In this paper, we develop…

In the last years, deep learning has dramatically improved the performances in a variety of medical image analysis applications. Among different types of deep learning models, convolutional neural networks have been among the most…

Deep neural networks (DNN) have shown great capacity of modeling a dynamical system; nevertheless, they usually do not obey physics constraints such as conservation laws. This paper proposes a new learning framework named ConCerNet to…