相关论文: Linear Separation via Optimism

Accurate calibration of probabilistic predictive models learned is critical for many practical prediction and decision-making tasks. There are two main categories of methods for building calibrated classifiers. One approach is to develop…

This paper presents a new approach to distributed linear filtering and prediction. The problem under consideration consists of a random dynamical system observed by a multi-agent network of sensors where the network is sparse. Inspired by…

Recently an algorithm, was discovered, which separates points in n-dimension by planes in such a manner that no two points are left un-separated by at least one plane{[}1-3{]}. By using this new algorithm we show that there are two ways of…

Under normality and homoscedasticity assumptions, Linear Discriminant Analysis (LDA) is known to be optimal in terms of minimising the Bayes error for binary classification. In the heteroscedastic case, LDA is not guaranteed to minimise…

We conducted an extensive computational experiment, lasting multiple CPU-years, to optimally select parameters for two important classes of algorithms for finding sparse solutions of underdetermined systems of linear equations. We make the…

We consider random instances of non-convex perceptron problems in the high-dimensional limit of a large number of examples $M$ and weights $N$, with finite load $\alpha = M/N$. We develop a formalism based on replica theory to predict the…

To reduce human error and prejudice, many high-stakes decisions have been turned over to machine algorithms. However, recent research suggests that this does not remove discrimination, and can perpetuate harmful stereotypes. While…

Logistic models are commonly used for binary classification tasks. The success of such models has often been attributed to their connection to maximum-likelihood estimators. It has been shown that gradient descent algorithm, when applied on…

The binary perceptron is the simplest artificial neural network formed by $N$ input units and one output unit, with the neural states and the synaptic weights all restricted to $\pm 1$ values. The task in the teacher--student scenario is to…

In this work, we present tensor-based linear and nonlinear models for hyperspectral data classification and analysis. By exploiting principles of tensor algebra, we introduce new classification architectures, the weight parameters of which…

Depth separation results propose a possible theoretical explanation for the benefits of deep neural networks over shallower architectures, establishing that the former possess superior approximation capabilities. However, there are no known…

We review the simplex method and two interior-point methods (the affine scaling and the primal-dual) for solving linear programming problems for checking avoiding sure loss, and propose novel improvements. We exploit the structure of these…

In various situations one is given only the predictions of multiple classifiers over a large unlabeled test data. This scenario raises the following questions: Without any labeled data and without any a-priori knowledge about the…

We consider the problem of exact recovery of a $k$-sparse binary vector from generalized linear measurements (such as logistic regression). We analyze the linear estimation algorithm (Plan, Vershynin, Yudovina, 2017), and also show…

Large-scale pre-trained language models such as BERT are popular solutions for text classification. Due to the superior performance of these advanced methods, nowadays, people often directly train them for a few epochs and deploy the…

We consider regression models involving multilayer perceptrons (MLP) with one hidden layer and a Gaussian noise. The estimation of the parameters of the MLP can be done by maximizing the likelihood of the model. In this framework, it is…

We consider the online multiclass linear classification under the bandit feedback setting. Beygelzimer, P\'{a}l, Sz\"{o}r\'{e}nyi, Thiruvenkatachari, Wei, and Zhang [ICML'19] considered two notions of linear separability, weak and strong…

Emerging applications of sensor networks for detection sometimes suggest that classical problems ought be revisited under new assumptions. This is the case of binary hypothesis testing with independent - but not necessarily identically…

Linear discrimination, from the point of view of numerical linear algebra, can be treated as solving an ill-posed system of linear equations. In order to generate a solution that is robust in the presence of noise, these problems require…

Unconstrained handwriting recognition is an essential task in document analysis. It is usually carried out in two steps. First, the document is segmented into text lines. Second, an Optical Character Recognition model is applied on these…