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Kernel-based methods enjoy powerful generalization capabilities in handling a variety of learning tasks. When such methods are provided with sufficient training data, broadly-applicable classes of nonlinear functions can be approximated…

We look at a stochastic time-varying optimization problem and we formulate online algorithms to find and track its optimizers in expectation. The algorithms are derived from the intuition that standard prediction and correction steps can be…

Optimization algorithms for solving nonconvex inverse problem have attracted significant interests recently. However, existing methods require the nonconvex regularization to be smooth or simple to ensure convergence. In this paper, we…

The perspective of developing trustworthy AI for critical applications in science and engineering requires machine learning techniques that are capable of estimating their own uncertainty. In the context of regression, instead of estimating…

Machine learning methods are used to discover complex nonlinear relationships in biological and medical data. However, sophisticated learning models are computationally unfeasible for data with millions of features. Here we introduce the…

Identifying the causal relationship among variables from observational data is an important yet challenging task. This work focuses on identifying the direct causes of an outcome and estimating their magnitude, i.e., learning the causal…

Deep learning has been applied to various tasks in the field of machine learning and has shown superiority to other common procedures such as kernel methods. To provide a better theoretical understanding of the reasons for its success, we…

Nonlinear regression problem is one of the most popular and important statistical tasks. The first methods like least squares estimation go back to Gauss and Legendre. Recent models and developments in statistics and machine learning like…

This paper proposes a novel regularization approach to bias Convolutional Neural Networks (CNNs) toward utilizing edge and line features in their hidden layers. Rather than learning arbitrary kernels, we constrain the convolution layers to…

The `Signal plus Noise' model for nonparametric regression can be extended to the case of observations taken at the vertices of a graph. This model includes many familiar regression problems. This article discusses the use of the edges of a…

Given observations of a physical system, identifying the underlying non-linear governing equation is a fundamental task, necessary both for gaining understanding and generating deterministic future predictions. Of most practical relevance…

Supervised learning by extreme learning machines resp. neural networks with random weights is studied under a non-stationary spatial-temporal sampling design which especially addresses settings where an autonomous object moving in a…

How to effectively approximate real-valued parameters with binary codes plays a central role in neural network binarization. In this work, we reveal an important fact that binarizing different layers has a widely-varied effect on the…

The highly non-linear nature of deep neural networks causes them to be susceptible to adversarial examples and have unstable gradients which hinders interpretability. However, existing methods to solve these issues, such as adversarial…

Function approximation has been an indispensable component in modern reinforcement learning algorithms designed to tackle problems with large state spaces in high dimensions. This paper reviews recent results on error analysis for these…

Latent variable models are an elegant framework for capturing rich probabilistic dependencies in many applications. However, current approaches typically parametrize these models using conditional probability tables, and learning relies…

Complex network reconstruction is a hot topic in many fields. Currently, the most popular data-driven reconstruction framework is based on lasso. However, it is found that, in the presence of noise, lasso loses efficiency for weighted…

An important characteristic of neural networks is their ability to learn representations of the input data with effective features for prediction, which is believed to be a key factor to their superior empirical performance. To better…

Neural models for NLP typically use large numbers of parameters to reach state-of-the-art performance, which can lead to excessive memory usage and increased runtime. We present a structure learning method for learning sparse,…

For data segmentation in high-dimensional linear regression settings, the regression parameters are often assumed to be sparse segment-wise, which enables many existing methods to estimate the parameters locally via $\ell_1$-regularised…