相关论文: Learning Set Functions that are Sparse in Non-Orth…

Fractional learning algorithms are trending in signal processing and adaptive filtering recently. However, it is unclear whether the proclaimed superiority over conventional algorithms is well-grounded or is a myth as their performance has…

Over the last three decades, function testing has been extensively studied over Boolean, finite fields, and discrete settings. However, to encode the real-world applications more succinctly, function testing over the reals (where the domain…

This paper studies offline reinforcement learning with linear function approximation in a setting with decision-theoretic, but not estimation sparsity. The structural restrictions of the data-generating process presume that the transitions…

In this paper we approximate high-dimensional functions $f\colon\mathbb T^d\to\mathbb C$ by sparse trigonometric polynomials based on function evaluations. Recently it was shown that a dimension-incremental sparse Fourier transform (SFT)…

Despite their attractiveness, popular perception is that techniques for nonparametric function approximation do not scale to streaming data due to an intractable growth in the amount of storage they require. To solve this problem in a…

A new line of research for feature selection based on neural networks has recently emerged. Despite its superiority to classical methods, it requires many training iterations to converge and detect informative features. The computational…

Machine learning of partial differential equations from data is a potential breakthrough to solve the lack of physical equations in complex dynamic systems, but because numerical differentiation is ill-posed to noise data, noise has become…

This paper concerns dictionary learning, i.e., sparse coding, a fundamental representation learning problem. We show that a subgradient descent algorithm, with random initialization, can provably recover orthogonal dictionaries on a natural…

Many transformations in deep learning architectures are sparsely connected. When such transformations cannot be designed by hand, they can be learned, even through plain backpropagation, for instance in attention mechanisms. However, during…

We study the problem of discovering functional dependencies (FD) from a noisy dataset. We focus on FDs that correspond to statistical dependencies in a dataset and draw connections between FD discovery and structure learning in…

In modern deep learning, algorithmic choices (such as width, depth, and learning rate) are known to modulate nuanced resource tradeoffs. This work investigates how these complexities necessarily arise for feature learning in the presence of…

Sparse dictionary coding represents signals as linear combinations of a few dictionary atoms. It has been applied to images, time series, graph signals and multi-way spatio-temporal data by jointly employing temporal and spatial…

Variational inference is becoming more and more popular for approximating intractable posterior distributions in Bayesian statistics and machine learning. Meanwhile, a few recent works have provided theoretical justification and new…

This paper aims to improve the feature learning in Convolutional Networks (Convnet) by capturing the structure of objects. A new sparsity function is imposed on the extracted featuremap to capture the structure and shape of the learned…

Set prediction is about learning to predict a collection of unordered variables with unknown interrelations. Training such models with set losses imposes the structure of a metric space over sets. We focus on stochastic and underdefined…

Extracting the underlying low-dimensional space where high-dimensional signals often reside has long been at the center of numerous algorithms in the signal processing and machine learning literature during the past few decades. At the same…

We propose a general deep architecture for learning functions on multiple permutation-invariant sets. We also show how to generalize this architecture to sets of elements of any dimension by dimension equivariance. We demonstrate that our…

Parity functions are fundamental Boolean operations with critical applications across machine learning, cryptography, and error correction. Yet, learning high-dimensional parity functions poses significant challenges: in a general setting,…

Despite their widespread success, the application of deep neural networks to functional data remains scarce today. The infinite dimensionality of functional data means standard learning algorithms can be applied only after appropriate…

Sparse sensor array selection arises in many engineering applications, where it is imperative to obtain maximum spatial resolution from a limited number of array elements. Recent research shows that computational complexity of array…