相关论文: Dimension Extractors and Optimal Decompression
Kucera and Gacs independently showed that every infinite sequence is Turing reducible to a Martin-Lof random sequence. This result is extended by showing that every infinite sequence S is Turing reducible to a Martin-Lof random sequence R…
This paper examines the constructive Hausdorff and packing dimensions of Turing degrees. The main result is that every infinite sequence S with constructive Hausdorff dimension dim_H(S) and constructive packing dimension dim_P(S) is Turing…
An extractor is a function that receives some randomness and either "improves" it or produces "new" randomness. There are statistical and algorithmical specifications of this notion. We study an algorithmical one called Kolmogorov…
We present an incremental, scalable and efficient dimension reduction technique for tensors that is based on sparse random linear coding. Data is stored in a compactified representation with fixed size, which makes memory requirements low…
Nonnegative Tucker decomposition (NTD) is a powerful tool for the extraction of nonnegative parts-based and physically meaningful latent components from high-dimensional tensor data while preserving the natural multilinear structure of…
Every real is computable from a Martin-Loef random real. This well known result in algorithmic randomness was proved by Kucera and Gacs. In this survey article we discuss various approaches to the problem of coding an arbitrary real into a…
Treedepth decomposition has several practical applications and can be used to speed up many parameterized algorithms. There are several works aiming to design a scalable algorithm to compute exact treedepth decompositions. Those include…
Most currently used tensor regression models for high-dimensional data are based on Tucker decomposition, which has good properties but loses its efficiency in compressing tensors very quickly as the order of tensors increases, say greater…
We introduce two nonlinear sufficient dimension reduction methods for regressions with tensor-valued predictors. Our goal is two-fold: the first is to preserve the tensor structure when performing dimension reduction, particularly the…
The Tucker decomposition, an extension of singular value decomposition for higher-order tensors, is a useful tool in analysis and compression of large-scale scientific data. While it has been studied extensively for static datasets, there…
Many features of dimensional reduction schemes are determined by the breaking of higher dimensional general covariance associated with the selection of a particular subset of coordinates. By investigating residual covariance we introduce…
Despite the recent success of deep learning models in numerous applications, their widespread use on mobile devices is seriously impeded by storage and computational requirements. In this paper, we propose a novel network compression method…
This article describes a technique of using a trigonometric function and combinatorial calculations to code or transform any finite sequence of binary numbers (0s and 1s) of any length to a unique set of three Real numbers. In reverse,…
Tensor decompositions are promising tools for big data analytics as they bring multiple modes and aspects of data to a unified framework, which allows us to discover complex internal structures and correlations of data. Unfortunately most…
Tensor train (TT) decomposition provides a space-efficient representation for higher-order tensors. Despite its advantage, we face two crucial limitations when we apply the TT decomposition to machine learning problems: the lack of…
This paper examines information-theoretic questions regarding the difficulty of compressing data versus the difficulty of decompressing data and the role that information loss plays in this interaction. Finite-state compression and…
With the increasing number of images and videos consumed by computer vision algorithms, compression methods are evolving to consider both perceptual quality and performance in downstream tasks. Traditional codecs can tackle this problem by…
A constructive version of Hausdorff dimension is developed using constructive supergales, which are betting strategies that generalize the constructive supermartingales used in the theory of individual random sequences. This constructive…
Dimensionality reduction is an essential technique for multi-way large-scale data, i.e., tensor. Tensor ring (TR) decomposition has become popular due to its high representation ability and flexibility. However, the traditional TR…
For classification problems, feature extraction is a crucial process which aims to find a suitable data representation that increases the performance of the machine learning algorithm. According to the curse of dimensionality theorem, the…