Low-rank Characteristic Tensor Density Estimation Part I: Foundations

• URL: http://arxiv.org/abs/2008.12315v2
• Date: Sat, 5 Jun 2021 03:06:33 GMT
• Title: Low-rank Characteristic Tensor Density Estimation Part I: Foundations
• Authors: Magda Amiridi, Nikos Kargas, Nicholas D. Sidiropoulos
• Abstract summary: We propose a novel approach that builds upon tensor factorization tools. In order to circumvent the curse of dimensionality, we introduce a low-rank model of this characteristic tensor. We demonstrate the very promising performance of the proposed method using several measured datasets.
• Score: 38.05393186002834
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Effective non-parametric density estimation is a key challenge in high-dimensional multivariate data analysis. In this paper,we propose a novel approach that builds upon tensor factorization tools. Any multivariate density can be represented by its characteristic function, via the Fourier transform. If the sought density is compactly supported, then its characteristic function can be approximated, within controllable error, by a finite tensor of leading Fourier coefficients, whose size de-pends on the smoothness of the underlying density. This tensor can be naturally estimated from observed realizations of the random vector of interest, via sample averaging. In order to circumvent the curse of dimensionality, we introduce a low-rank model of this characteristic tensor, which significantly improves the density estimate especially for high-dimensional data and/or in the sample-starved regime. By virtue of uniqueness of low-rank tensor decomposition, under certain conditions, our method enables learning the true data-generating distribution. We demonstrate the very promising performance of the proposed method using several measured datasets.

Related papers

• Regulating Model Reliance on Non-Robust Features by Smoothing Input Marginal Density [93.32594873253534]
  Trustworthy machine learning requires meticulous regulation of model reliance on non-robust features. We propose a framework to delineate and regulate such features by attributing model predictions to the input.
  arXiv  Detail & Related papers  (2024-07-05T09:16:56Z)
• TERM Model: Tensor Ring Mixture Model for Density Estimation [48.622060998018206]
  In this paper, we take tensor ring decomposition for density estimator, which significantly reduces the number of permutation candidates. A mixture model that incorporates multiple permutation candidates with adaptive weights is further designed, resulting in increased expressive flexibility. This approach acknowledges that suboptimal permutations can offer distinctive information besides that of optimal permutations.
  arXiv  Detail & Related papers  (2023-12-13T11:39:56Z)
• Anomaly Detection with Variance Stabilized Density Estimation [49.46356430493534]
  We present a variance-stabilized density estimation problem for maximizing the likelihood of the observed samples. To obtain a reliable anomaly detector, we introduce a spectral ensemble of autoregressive models for learning the variance-stabilized distribution. We have conducted an extensive benchmark with 52 datasets, demonstrating that our method leads to state-of-the-art results.
  arXiv  Detail & Related papers  (2023-06-01T11:52:58Z)
• Generative Modeling via Hierarchical Tensor Sketching [12.005736675688917]
  We propose a hierarchical tensor-network approach for approximating high-dimensional probability density via empirical distribution. The complexity of the resulting algorithm scales linearly in the dimension of the high-dimensional density.
  arXiv  Detail & Related papers  (2023-04-11T15:55:13Z)
• High-dimensional density estimation with tensorizing flow [5.457842083043014]
  We propose the tensorizing flow method for estimating high-dimensional probability density functions from the observed data. The proposed method combines the optimization-less feature of the tensor-train with the flexibility of the flow-based generative models.
  arXiv  Detail & Related papers  (2022-12-01T18:45:45Z)
• Error Analysis of Tensor-Train Cross Approximation [88.83467216606778]
  We provide accuracy guarantees in terms of the entire tensor for both exact and noisy measurements. Results are verified by numerical experiments, and may have important implications for the usefulness of cross approximations for high-order tensors.
  arXiv  Detail & Related papers  (2022-07-09T19:33:59Z)
• Density-Based Clustering with Kernel Diffusion [59.4179549482505]
  A naive density corresponding to the indicator function of a unit $d$-dimensional Euclidean ball is commonly used in density-based clustering algorithms. We propose a new kernel diffusion density function, which is adaptive to data of varying local distributional characteristics and smoothness.
  arXiv  Detail & Related papers  (2021-10-11T09:00:33Z)
• Large-Scale Learning with Fourier Features and Tensor Decompositions [3.6930948691311007]
  We exploit the tensor product structure of deterministic Fourier features, which enables us to represent the model parameters as a low-rank tensor decomposition. We demonstrate by means of numerical experiments how our low-rank tensor approach obtains the same performance of the corresponding nonparametric model.
  arXiv  Detail & Related papers  (2021-09-03T14:12:53Z)
• Low-rank Characteristic Tensor Density Estimation Part II: Compression and Latent Density Estimation [31.631861197477185]
  Learning generative probabilistic models is a core problem in machine learning. This paper proposes a joint dimensionality reduction and non-parametric density estimation framework. We demonstrate that the proposed model achieves very promising results on regression tasks, sampling, and anomaly detection.
  arXiv  Detail & Related papers  (2021-06-20T00:38:56Z)
• Improving Nonparametric Density Estimation with Tensor Decompositions [14.917420021212912]
  Nonparametric density estimators often perform well on low dimensional data, but suffer when applied to higher dimensional data. This paper investigates whether these improvements can be extended to other simplified dependence assumptions. We prove that restricting estimation to low-rank nonnegative PARAFAC or Tucker decompositions removes the dimensionality exponent on bin width rates for multidimensional histograms.
  arXiv  Detail & Related papers  (2020-10-06T01:39:09Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.