arXiv research

The paper explores when and why value decomposition algorithms work in cooperative multi-agent reinforcement learning.

The paper uncovers the mathematical structure enabling value decomposition in multi-agent systems.

The paper develops axioms for uniquely decomposing functions with real arguments.

Decomposing tensors into orthogonal factors is a well-known task in statistics, machine learning, and signal processing. We study orthogonal outer product decompositions where the factors in the summands in the decomposition are required to be orthogonal across summands, by relating this orthogonal decomposition to the…

Singular Value Decomposition (SVD) constitutes a bridge between the linear algebra concepts and multi-layer neural networks---it is their linear analogy. Besides of this insight, it can be used as a good initial guess for the network parameters, leading to substantially better optimization results.

We solve the ANOVA decomposition for categorical inputs.

New method decomposes profits and losses continuously, avoiding discrete reporting issues.

Paper tackles tensor decomposition for unaligned observations using RKHS and novel loss functions.

We discuss multiscale representations of discrete manifold-valued data. As it turns out that we cannot expect general manifold-analogues of biorthogonal wavelets to possess perfect reconstruction, we focus our attention on those constructions which are based on upscaling operators which are either interpolating or midp…

This work studies the linear approximation of high-dimensional dynamical systems using low-rank dynamic mode decomposition (DMD). Searching this approximation in a data-driven approach is formalised as attempting to solve a low-rank constrained optimisation problem. This problem is non-convex and state-of-the-art algor…

AL$\ell_0$CORE tensor decomposition reduces computational cost for sparse count data.

Distributed model training suffers from communication overheads due to frequent gradient updates transmitted between compute nodes. To mitigate these overheads, several studies propose the use of sparsified stochastic gradients. We argue that these are facets of a general sparsification method that can operate on any p…

The paper proposes and discusses semiorthogonal decompositions for moduli spaces of vector bundles.

Singular value decomposition (SVD) is the mathematical basis of principal component analysis (PCA). Together, SVD and PCA are one of the most widely used mathematical formalism/decomposition in machine learning, data mining, pattern recognition, artificial intelligence, computer vision, signal processing, etc. In recen…

Study uncovers complex critical points in tensor decomposition.

Fast and accurate methods for low-rank learning problems.

In this article, we consider the sparse tensor singular value decomposition, which aims for dimension reduction on high-dimensional high-order data with certain sparsity structure. A method named Sparse Tensor Alternating Thresholding for Singular Value Decomposition (STAT-SVD) is proposed. The proposed procedure featu…

We compared the regular Singular Value Decomposition (SVD), truncated SVD, Krylov method and Randomized PCA, in terms of time and space complexity. It is well-known that Krylov method and Randomized PCA only performs well when k << n, i.e. the number of eigenpair needed is far less than that of matrix size. We compared…

New hyperbolic 4-manifolds found with special functions.

Study evaluates thresholds for removing noise from DNN weights using random matrix theory.

Unified local and global explanations through functional decomposition of low dimensional structures.

Derives a primal-dual MLSVD formulation for multilinear data.

The study examines how different interpolation methods affect the decomposition of life insurance surplus.

FreDN separates trends and periodicities in non-stationary time series forecasts.

Two methods preserve tensor structure for reduced dimensionality in tensor regression.

Extends a theorem for first-order elliptic operators on manifolds.

We extend the randomized singular value decomposition (SVD) algorithm \citep{Halko2011finding} to estimate the SVD of a shifted data matrix without explicitly constructing the matrix in the memory. With no loss in the accuracy of the original algorithm, the extended algorithm provides for a more efficient way of matrix…

A new PCR method using SVD with sparse regularization.

Value functions are crucial for model-free Reinforcement Learning (RL) to obtain a policy implicitly or guide the policy updates. Value estimation heavily depends on the stochasticity of environmental dynamics and the quality of reward signals. In this paper, we propose a two-step understanding of value estimation from…

In this note, we report the back propagation formula for complex valued singular value decompositions (SVD). This formula is an important ingredient for a complete automatic differentiation(AD) infrastructure in terms of complex numbers, and it is also the key to understand and utilize AD in tensor networks.

Q-SHAP efficiently calculates feature contributions in boosting trees.

In this paper, we study the possibility of inferring early warning indicators (EWIs) for periods of extreme bitcoin price volatility using features obtained from Bitcoin daily transaction graphs. We infer the low-dimensional representations of transaction graphs in the time period from 2012 to 2017 using Bitcoin blockc…

Informed by recent work on tensor singular value decomposition and circulant algebra matrices, this paper presents a new theoretical bridge that unifies the hypercomplex and tensor-based approaches to singular value decomposition and robust principal component analysis. We begin our work by extending the principal comp…

Agent maximizes utility with pathwise constraint on portfolio value.

Reproducing kernel Hilbert spaces (RKHSs) play an important role in many statistics and machine learning applications ranging from support vector machines to Gaussian processes and kernel embeddings of distributions. Operators acting on such spaces are, for instance, required to embed conditional probability distributi…

Fast matrix algorithms have become the fundamental tools of machine learning in big data era. The generalized matrix regression problem is widely used in the matrix approximation such as CUR decomposition, kernel matrix approximation, and stream singular value decomposition (SVD), etc. In this paper, we propose a fast …

High throughput biomedical measurements normally capture multiple overlaid biologically relevant signals and often also signals representing different types of technical artefacts like e.g. batch effects. Signal identification and decomposition are accordingly main objectives in statistical biomedical modeling and data…

Methods based on vector embeddings of knowledge graphs have been actively pursued as a promising approach to knowledge graph completion.However, embedding models generate storage-inefficient representations, particularly when the number of entities and relations, and the dimensionality of the real-valued embedding vect…

Physics-inspired methods optimize SVD compression of LLMs.

This work improves tensor decomposition methods, especially for large datasets.

In this paper we study the Föllmer-Schweizer decomposition of a square integrable random variable $ξ$ with respect to a given semimartingale $S$ under restricted information. Thanks to the relationship between this decomposition and that of the projection of $ξ$ with respect to the given information flow, we characteri…

Efficient algorithm for Hadamard decomposition of matrices.

The paper sharpens the analysis of sketch-and-project methods using randomized singular value decomposition.

The target of this paper is to establish the bid-ask pricing frame work for the American contingent claims against risky assets with G-asset price systems (see \cite{Chen2013b}) on the financial market under Knight uncertainty. First, we prove G-Dooby-Meyer decomposition for G-supermartingale. Furthermore, we consider …

Tensor decompositions have rich applications in statistics and machine learning, and developing efficient, accurate algorithms for the problem has received much attention recently. Here, we present a new method built on Kruskal's uniqueness theorem to decompose symmetric, nearly orthogonally decomposable tensors. Unlik…

This work considers a computationally and statistically efficient parameter estimation method for a wide class of latent variable models---including Gaussian mixture models, hidden Markov models, and latent Dirichlet allocation---which exploits a certain tensor structure in their low-order observable moments (typically…

New insights into X-ray transform on hyperbolic disk, with functional relations and range characterizations.

We factorize harmonic maps with values in a semisimple Lie groups in a product of harmonic maps with values in the components of the Iwasawa decomposition. In particular, we use this factorization to study the harmonic maps from $\mathbb{R}^n$ into $SL(2,\mathbb{R})$.