相关论文: Efficient learning of simplices

Most systems and learning algorithms optimize average performance or average loss -- one reason being computational complexity. However, many objectives of practical interest are more complex than simply average loss. This arises, for…

In this article, we develop efficient sampling algorithms for random surjections from $[n]$ to $[k]$ for all $n \geq k$. We make no assumption about $n$ and $k$. In particular, we do not make the common assumption that the ratio…

We consider the problem of uniform sampling of points on an algebraic variety. Specifically, we develop a randomized algorithm that, given a small set of multivariate polynomials over a sufficiently large finite field, produces a common…

In this paper, we propose an improved numerical algorithm for solving minimax problems based on nonsmooth optimization, quadratic programming and iterative process. We also provide a rigorous proof of convergence for our algorithm under…

Episodic training is a core ingredient of few-shot learning to train models on tasks with limited labelled data. Despite its success, episodic training remains largely understudied, prompting us to ask the question: what is the best way to…

In this paper we derive an efficient algorithm to learn the parameters of structured predictors in general graphical models. This algorithm blends the learning and inference tasks, which results in a significant speedup over traditional…

Independent component analysis (ICA) has become a standard data analysis technique applied to an array of problems in signal processing and machine learning. This tutorial provides an introduction to ICA based on linear algebra formulating…

Independent Component Analysis (ICA) is a technique for unsupervised exploration of multi-channel data widely used in observational sciences. In its classical form, ICA relies on modeling the data as a linear mixture of non-Gaussian…

In structured prediction problems where we have indirect supervision of the output, maximum marginal likelihood faces two computational obstacles: non-convexity of the objective and intractability of even a single gradient computation. In…

High-dimensional data is common in multiple areas, such as health care and genomics, where the number of features can be tens of thousands. In such scenarios, the large number of features often leads to inefficient learning. Constraint…

We consider the problem of uncertainty quantification in change point regressions, where the signal can be piecewise polynomial of arbitrary but fixed degree. That is we seek disjoint intervals which, uniformly at a given confidence level,…

Independent Component Analysis (ICA) is a foundational tool for unsupervised representation learning, yet its high-dimensional theory remains largely limited to single-component recovery. We develop an asymptotically exact mean-field theory…

A central problem in unsupervised deep learning is how to find useful representations of high-dimensional data, sometimes called "disentanglement". Most approaches are heuristic and lack a proper theoretical foundation. In linear…

We propose a simple and efficient algorithm for learning sparse invariant representations from unlabeled data with fast inference. When trained on short movies sequences, the learned features are selective to a range of orientations and…

Let us assume that $f$ is a continuous function defined on the unit ball of $\mathbb R^d$, of the form $f(x) = g (A x)$, where $A$ is a $k \times d$ matrix and $g$ is a function of $k$ variables for $k \ll d$. We are given a budget $m \in…

Motivated by the limitation of analyzing oscillatory signals composed of multiple components with fast-varying instantaneous frequency, we approach the time-frequency analysis problem by optimization. Based on the proposed adaptive harmonic…

We give an algorithm for learning a mixture of {\em unstructured} distributions. This problem arises in various unsupervised learning scenarios, for example in learning {\em topic models} from a corpus of documents spanning several topics.…

We design a new, fast algorithm for agnostically learning univariate probability distributions whose densities are well approximated by piecewise polynomial functions. Let $f$ be the density function of an arbitrary univariate distribution,…

For many machine learning problems, data is abundant and it may be prohibitive to make multiple passes through the full training set. In this context, we investigate strategies for dynamically increasing the effective sample size, when…

Graphical models are useful tools for describing structured high-dimensional probability distributions. Development of efficient algorithms for learning graphical models with least amount of data remains an active research topic.…