相关论文: Learning single-index models via harmonic decompos…

We propose a novel classification framework grounded in symbolic dynamics and data compression using chaotic maps. The core idea is to model each class by generating symbolic sequences from thresholded real-valued training data, which are…

Abstract notions of convexity over the vertices of a graph, and corresponding notions of halfspaces, have recently gained attention from the machine learning community. In this work we study monophonic halfspaces, a notion of graph…

In traditional models of supervised learning, the goal of a learner -- given examples from an arbitrary joint distribution on $\mathbb{R}^d \times \{\pm 1\}$ -- is to output a hypothesis that is competitive (to within $\epsilon$) of the…

Hamiltonian systems are differential equations which describe systems in classical mechanics, plasma physics, and sampling problems. They exhibit many structural properties, such as a lack of attractors and the presence of conservation…

One of the major problems in modeling natural signals is that signals with very similar structure may locally have completely different measurements, e.g., images taken under different illumination conditions, or the speech signal captured…

In this work we consider generic Gaussian Multi-index models, in which the labels only depend on the (Gaussian) $d$-dimensional inputs through their projection onto a low-dimensional $r = O_d(1)$ subspace, and we study efficient agnostic…

Reconstructing continuous signals from a small number of discrete samples is a fundamental problem across science and engineering. In practice, we are often interested in signals with 'simple' Fourier structure, such as bandlimited,…

Linear regression studies the problem of estimating a model parameter $\beta^* \in \mathbb{R}^p$, from $n$ observations $\{(y_i,\mathbf{x}_i)\}_{i=1}^n$ from linear model $y_i = \langle \mathbf{x}_i,\beta^* \rangle + \epsilon_i$. We…

A flexible recommendation and retrieval system requires music similarity in terms of multiple partial elements of musical pieces to allow users to select the element they want to focus on. A method for music similarity learning using…

For challenging machine learning problems such as zero-shot learning and fine-grained categorization, embedding learning is the machinery of choice because of its ability to learn generic notions of similarity, as opposed to class-specific…

We introduce a learning-based algorithm to obtain a measurement matrix for compressive sensing related recovery problems. The focus lies on matrices with a constant modulus constraint which typically represent a network of analog phase…

We present a method for training multi-label, massively multi-class image classification models, that is faster and more accurate than supervision via a sigmoid cross-entropy loss (logistic regression). Our method consists in embedding…

In the classical source coding problem, the compressed source is reconstructed at the decoder with respect to some distortion metric. Motivated by settings in which we are interested in more than simply reconstructing the compressed source,…

We study the unlabeled sensing problem that aims to solve a linear system of equations $A x =\pi(y) $ for an unknown permutation $\pi$. For a generic matrix $A$ and a generic vector $y$, we construct a system of polynomial equations whose…

In this paper, we consider the problem of estimating self-tuning histograms using query workloads. To this end, we propose a general learning theoretic formulation. Specifically, we use query feedback from a workload as training data to…

We consider the landscape of empirical risk minimization for high-dimensional Gaussian single-index models (generalized linear models). The objective is to recover an unknown signal $\boldsymbol{\theta}^\star \in \mathbb{R}^d$ (where $d \gg…

Consider measuring an n-dimensional vector x through the inner product with several measurement vectors, a_1, a_2, ..., a_m. It is common in both signal processing and statistics to assume the linear response model y_i = <a_i, x> + e_i,…

Whole slide images, with their gigapixel-scale panoramas of tissue samples, are pivotal for precise disease diagnosis. However, their analysis is hindered by immense data size and scarce annotations. Existing MIL methods face challenges due…

The problem of learning single index and multi index models has gained significant interest as a fundamental task in high-dimensional statistics. Many recent works have analysed gradient-based methods, particularly in the setting of…

Singular statistical models-including mixtures, matrix factorization, and neural networks-violate regular asymptotics due to parameter non-identifiability and degenerate Fisher geometry. Although singular learning theory characterizes…