Related papers: Dimension Extractors and Optimal Decompression
Models of physics beyond the Standard Model often contain a large number of parameters. These form a high-dimensional space that is computationally intractable to fully explore. Experimental constraints project onto a subspace of viable…
We strengthen the notion of "double samplers", first introduced by Dinur and Kaufman [Proc. 58th FOCS, 2017], which are samplers with additional combinatorial properties, and whose existence we prove using high dimensional expanders. The…
A classic result in algorithmic information theory is that every infinite binary sequence is computable from a Martin-Loef random infinite binary sequence. Proved independently by Kucera and Gacs, this result answered a question by Charles…
Tensor Factor Models (TFM) are appealing dimension reduction tools for high-order large-dimensional tensor time series, and have wide applications in economics, finance and medical imaging. In this paper, we propose a projection estimator…
In this paper, we present improved decoding algorithms for expander-based Tanner codes. We begin by developing a randomized linear-time decoding algorithm that, under the condition that $ \delta d_0 > 2 $, corrects up to $ \alpha n $ errors…
In this paper we introduce a general theory for nonlinear sufficient dimension reduction, and explore its ramifications and scope. This theory subsumes recent work employing reproducing kernel Hilbert spaces, and reveals many parallels…
In this paper, we study optimal estimates and comparison of the coefficients in the Gegenbauer series expansion. We propose an alternative derivation of the contour integral representation of the Gegenbauer expansion coefficients which was…
Solving large scale Optimal Transport (OT) in machine learning typically relies on sampling measures to obtain a tractable discrete problem. While the discrete solver's accuracy is controllable, the rate of convergence of the discretization…
We derive computationally tractable methods to select a small subset of experiment settings from a large pool of given design points. The primary focus is on linear regression models, while the technique extends to generalized linear models…
Data compression has been widely applied in many data processing areas. Compression methods use variable-size codes with the shorter codes assigned to symbols or groups of symbols that appear in the data frequently. Fibonacci coding, as a…
We present a collection of algorithms which utilize dimensional reduction to perform mesh refinement and study possibly singular solutions of time-dependent partial differential equations. The algorithms are inspired by constructions used…
Contraction analysis establishes exponential incremental convergence of a nonlinear system by solving a linear matrix inequality for a contraction metric, and has become a standard resource for solving problems in nonlinear control and…
Tensor networks provide compact and scalable representations of high-dimensional data, enabling efficient computation in fields such as quantum physics, numerical partial differential equations (PDEs), and machine learning. This paper…
We develop the theory of the additive dimension ${\rm dim} (A)$, i.e. the size of a maximal dissociated subset of a set $A$. It was shown that the additive dimension is closely connected with the growth of higher sumsets $nA$ of our set…
The Johnson-Lindenstrauss transform is a fundamental method for dimension reduction in Euclidean spaces, that can map any dataset of $n$ points into dimension $O(\log n)$ with low distortion of their distances. This dimension bound is tight…
This paper studies simultaneous feature selection and extraction in supervised and unsupervised learning. We propose and investigate selective reduced rank regression for constructing optimal explanatory factors from a parsimonious subset…
Large tensors are frequently encountered in various fields such as computer vision, scientific simulations, sensor networks, and data mining. However, these tensors are often too large for convenient processing, transfer, or storage.…
An encoder wishes to minimize the bit rate necessary to guarantee that a decoder is able to calculate a symbol-wise function of a sequence available only at the encoder and a sequence that can be measured only at the decoder. This classical…
The Ku\v{c}era--G\'{a}cs theorem is a fundamental result in algorithmic randomness. It states that every infinite sequence $X$ is Turing reducible to a Martin-L\"of random $R$. This paper studies resource-bounded analogues of the…
Low-rank approximation of tensors has been widely used in high-dimensional data analysis. It usually involves singular value decomposition (SVD) of large-scale matrices with high computational complexity. Sketching is an effective data…