相关论文: Analyzing Deviations of Dyadic Lines in Fast Hough…

We consider shallow (single hidden layer) neural networks and characterize their performance when trained with stochastic gradient descent as the number of hidden units $N$ and gradient descent steps grow to infinity. In particular, we…

This paper investigates the problem of dim frequency line detection and recovery in the so-called lofargram. Theoretically, time integration long enough can always enhance the detection characteristic. But this does not hold for irregularly…

We consider the problem of anomaly detection in images, and present a new detection technique. Given a sample of images, all known to belong to a "normal" class (e.g., dogs), we show how to train a deep neural model that can detect…

How do real graphs evolve over time? What are ``normal'' growth patterns in social, technological, and information networks? Many studies have discovered patterns in static graphs, identifying properties in a single snapshot of a large…

We propose to use the concept of the Hamming bound to derive the optimal criteria for learning hash codes with a deep network. In particular, when the number of binary hash codes (typically the number of image categories) and code length…

It is becoming increasingly common in regression to train neural networks that model the entire distribution even if only the mean is required for prediction. This additional modeling often comes with performance gain and the reasons behind…

We consider the Random Walk Metropolis algorithm on $\mathbb{R}^n$ with Gaussian proposals, and when the target probability measure is the $n$-fold product of a one-dimensional law. It is well known (see Roberts et al. (Ann. Appl. Probab. 7…

Drift analysis has become a powerful tool to prove bounds on the runtime of randomized search heuristics. It allows, for example, fairly simple proofs for the classical problem how the (1+1) Evolutionary Algorithm (EA) optimizes an…

Recent years have witnessed significant progress in developing effective training and fast sampling techniques for diffusion models. A remarkable advancement is the use of stochastic differential equations (SDEs) and their…

Large deviation results are given for a class of perturbed nonhomogeneous Markov chains on finite state space which formally includes some stochastic optimization algorithms. Specifically, let {P_n} be a sequence of transition matrices on a…

Line detection is a basic digital image processing operation used by higher-level processing methods. Recently, transformer-based methods for line detection have proven to be more accurate than methods based on CNNs, at the expense of…

Robust statistics aims to compute quantities to represent data where a fraction of it may be arbitrarily corrupted. The most essential statistic is the mean, and in recent years, there has been a flurry of theoretical advancement for…

An orthogonal Haar scattering transform is a deep network, computed with a hierarchy of additions, subtractions and absolute values, over pairs of coefficients. It provides a simple mathematical model for unsupervised deep network learning.…

Consider the Allen-Cahn equation on the $d$-dimensional torus, $d=2,3$, in the sharp interface limit. As it is well known, the limiting dynamics is described by the motion by mean curvature of the interface between the two stable phases.…

Recently, many studies have shed light on the high adaptivity of deep neural network methods in nonparametric regression models, and their superior performance has been established for various function classes. Motivated by this…

We study the fundamental problem of high-dimensional mean estimation in a robust model where a constant fraction of the samples are adversarially corrupted. Recent work gave the first polynomial time algorithms for this problem with…

We consider a class of pattern matching problems where a normalising transformation is applied at every alignment. Normalised pattern matching plays a key role in fields as diverse as image processing and musical information processing…

Most of the classical approaches to straight line detection only deal with a binary edge image and need to use 2D interpolation operation. This paper proposes a new transform method figuratively named as funnel transform which can…

Computational complexity and approximation algorithms are reported for a problem of stabbing a set of straight line segments with the least cardinality set of disks of fixed radii $r>0$ where the set of segments forms a straight line…

Unlike the conventional wisdom in statistical learning theory, the test error of a deep neural network (DNN) often demonstrates double descent: as the model complexity increases, it first follows a classical U-shaped curve and then shows a…