# Generalization bounds for sparse random feature expansions

@article{Hashemi2022GeneralizationBF, title={Generalization bounds for sparse random feature expansions}, author={Abolfazl Hashemi and Hayden Schaeffer and Robert Shi and Ufuk Topcu and Giang Tran and Rachel A. Ward}, journal={Applied and Computational Harmonic Analysis}, year={2022} }

## 10 Citations

### Conditioning of Random Feature Matrices: Double Descent and Generalization Error

- Computer ScienceArXiv
- 2021

It is proved that the risk associated with regression problems using a random feature matrix exhibits thedouble descent phenomenon and that this is an effect of the double descent behavior of the condition number.

### HARFE: Hard-Ridge Random Feature Expansion

- Computer ScienceArXiv
- 2022

It is proved that the HARFE method is guaranteed to converge with a given error bound depending on the noise and the parameters of the sparse ridge regression model.

### SHRIMP: Sparser Random Feature Models via Iterative Magnitude Pruning

- Computer ScienceArXiv
- 2021

It is shown that SHRIMP obtains better than or competitive test accuracy compared to state-of-art sparse feature and additive methods such as SRFE-S, SSAM, and SALSA and is robust to the pruning rate, indicating a robustness in the structure of the obtained subnetworks.

### Towards optimal sampling for learning sparse approximation in high dimensions

- Computer Science, MathematicsArXiv
- 2022

This chapter discusses recent work on learning sparse approximations to high-dimensional functions on data, where the target functions may be scalar-, vectoror even Hilbert space-valued, and describes a general construction of sampling measures that improves over standard Monte Carlo sampling.

### Concentration of Random Feature Matrices in High-Dimensions

- Computer Science, MathematicsArXiv
- 2022

This work shows that the singular values of random feature matrices concentrate near their full expectation and near one with high-probability, and since the dimension depends only on the logarithm of the number of random weights or thenumber of data points, complexity bounds can be achieved even in moderate dimensions for many practical setting.

### Learning Sparse Mixture Models

- Computer Science
- 2022

This work approximates high-dimensional density functions with an ANOVA-like sparse structure by the mixture of wrapped Gaussian and von Mises distributions by developing an algorithm that determines the mixture model’s set of active variables by the Kolmogorov-Smirnov and correlation test.

### Sparse mixture models inspired by ANOVA decompositions

- Computer Science, MathematicsETNA - Electronic Transactions on Numerical Analysis
- 2021

Inspired by the analysis of variance (ANOVA) decomposition of functions, we propose a Gaussianuniform mixture model on the high-dimensional torus which relies on the assumption that the function that…

### Renormalized Sparse Neural Network Pruning

- Computer ScienceArXiv
- 2022

It is proven that the renormalizing sparse neural networks method’s error converges to zero as network parameters cluster or concentrate, and it is proved that without renormalization, the error does not converge to zero in general.

### Structured random receptive fields enable informative sensory encodings

- Computer Science, BiologybioRxiv
- 2021

This work model neuronal receptive fields as random, variable samples from parameterized distributions and demonstrates this model in two sensory modalities using data from insect mechanosensors and mammalian primary visual cortex, leading to a significant theoretical connection between the foundational concepts of receptive fields and random features, a leading theory for understanding artificial neural networks.

### SRMD: Sparse Random Mode Decomposition

- Computer ScienceArXiv
- 2022

This work proposed a random feature method for analyzing time-series data by constructing a sparse approximation to the spectrogram that outperforms other state-of-the-art decomposition methods.

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