Related papers: Lecture Notes: Selected topics on robust statistic…

In a series of recent work, we have introduced a general framework for quantitative reasoning in specification theories. The contribution of this paper is to show how this framework can be applied to yield a robust specification theory for…

Tensor regression is an important tool for tensor data analysis, but existing works have not considered the impact of outliers, making them potentially sensitive to such data points. This paper proposes a low tubal rank robust regression…

We present the first learning-augmented data structure for implementing dictionaries with optimal consistency and robustness. Our data structure, named RobustSL, is a skip list augmented by predictions of access frequencies of elements in a…

Despite their numerous successes, there are many scenarios where adversarial risk metrics do not provide an appropriate measure of robustness. For example, test-time perturbations may occur in a probabilistic manner rather than being…

Deep learning has arguably achieved tremendous success in recent years. In simple words, deep learning uses the composition of many nonlinear functions to model the complex dependency between input features and labels. While neural networks…

Neural networks are an indispensable model class for many complex learning tasks. Despite the popularity and importance of neural networks and many different established techniques from literature for stabilization and robustification of…

Ordinary least-squares (OLS) estimators for a linear model are very sensitive to unusual values in the design space or outliers among y values. Even one single atypical value may have a large effect on the parameter estimates. This article…

This is a self-contained set of lecture notes covering various aspects of the theory of open quantum system, at a level appropriate for a one-semester graduate course. The main emphasis is on completely positive maps and master equations,…

An emerging problem in trustworthy machine learning is to train models that produce robust interpretations for their predictions. We take a step towards solving this problem through the lens of axiomatic attribution of neural networks. Our…

In recent years numerous methods have been developed to formally verify the robustness of deep neural networks (DNNs). Though the proposed techniques are effective in providing mathematical guarantees about the DNNs behavior, it is not…

These Lecture Notes are devoted to an introductory description of some of the most widely applied statistical methods for the analysis of the Large-Scale Structure (LSS) of the Universe. Rather than providing technical details about the…

These notes derive a number of technical results on nonlinear contraction theory, a comparatively recent tool for system stability analysis. In particular, they provide new results on the preservation of contraction through system…

These lecture notes concern information-theoretic notions of entropy. They are intended for, and have been successfully taught to, undergraduate students interested inresearch careers. Besides basic notions of analysis related to…

Despite deep recurrent neural networks (RNNs) demonstrate strong performance in text classification, training RNN models are often expensive and requires an extensive collection of annotated data which may not be available. To overcome the…

This textbook covers principles behind main modern deep reinforcement learning algorithms that achieved breakthrough results in many domains from game AI to robotics. All required theory is explained with proofs using unified notation and…

Learning representations of data is an important problem in statistics and machine learning. While the origin of learning representations can be traced back to factor analysis and multidimensional scaling in statistics, it has become a…

The purpose of this paper is to look into how central notions in statistical learning theory, such as realisability, generalise under the assumption that train and test distribution are issued from the same credal set, i.e., a convex set of…

The problem of statistical learning is to construct an accurate predictor of a random variable as a function of a correlated random variable on the basis of an i.i.d. training sample from their joint distribution. Allowable predictors are…

Time series forecasting is an important and forefront task in many real-world applications. However, most of time series forecasting techniques assume that the training data is clean without anomalies. This assumption is unrealistic since…

Deep neural networks have achieved remarkable results across many language processing tasks, however these methods are highly sensitive to noise and adversarial attacks. We present a regularization based method for limiting network…