arXiv research

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

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.

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

New hyperbolic 4-manifolds found with special functions.

We solve the ANOVA decomposition for categorical inputs.

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

Study uncovers complex critical points in tensor decomposition.

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…

Adaptive tensor modeling preserves continuity in multidimensional data.

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

Physics-inspired methods optimize SVD compression of LLMs.

Generalizes Hoeffding's decomposition for dependent inputs under mild conditions.

We study regularity properties of the dynamic value functions of primal and dual problems of optimal investing for utility functions defined on the whole real line. Relations between decomposition terms of value processes of primal and dual problems and between optimal solutions of basic and conditional utility maximiz…

We provide a unified view of additive explanations for dependent inputs.

Proposes FOAGP for efficient orthogonal effect decomposition of black-box computer experiments.

New method combines value function decomposition and policy gradients for cooperative multi-agent reinforcement learning.

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 …

Stochastic discount factor (SDF) processes in dynamic economies admit a permanent-transitory decomposition in which the permanent component characterizes pricing over long investment horizons. This paper introduces an empirical framework to analyze the permanent-transitory decomposition of SDF processes. Specifically, …

Q($Δ$)-Learning improves Q-Learning by separating action-value functions into different time scales.

We present a novel method for learning a set of disentangled reward functions that sum to the original environment reward and are constrained to be independently obtainable. We define independent obtainability in terms of value functions with respect to obtaining one learned reward while pursuing another learned reward…

TreeHFD algorithm explains tree ensemble models through hierarchical orthogonality.

New matrix approximation method using RBF components for better memory efficiency.

A new PCR method using SVD with sparse regularization.

Paper proposes a new optimization framework for learning eigenfunctions of operators.

We show that Scherk's first surface, a one-parameter family of solutions to the minimal surface equation, may be written as a linear superposition of other solutions with specific parametric values.

STRIDE improves explainable AI by efficiently decomposing feature interactions without subset enumeration.

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…

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

Generalizes randomized SVD for better matrix approximations using Gaussian vectors.

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…

A new multi-agent learning method improves performance in complex games.

Regularized empirical risk minimization with constrained labels (in contrast to fixed labels) is a remarkably general abstraction of learning. For common loss and regularization functions, this optimization problem assumes the form of a mixed integer program (MIP) whose objective function is non-convex. In this form, t…

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…

Variables in many massive high-dimensional data sets are structured, arising for example from measurements on a regular grid as in imaging and time series or from spatial-temporal measurements as in climate studies. Classical multivariate techniques ignore these structural relationships often resulting in poor performa…

Study introduces indecomposability for varifolds, leading to geometric consequences.

Generalizes PCA and ICA for continuous-time signals using neural networks.

Flattenings of knotted surfaces help define new invariants.

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.

Enhanced Bruhat decomposition studies Morse theory and Reidemeister torsion.

Previous work in hierarchical reinforcement learning has faced a dilemma: either ignore the values of different possible exit states from a subroutine, thereby risking suboptimal behavior, or represent those values explicitly thereby incurring a possibly large representation cost because exit values refer to nonlocal a…

For a one-parameter family of simple metrics of constant curvature ($4κ$ for $κ\in (-1,1)$) on the unit disk $M$, we first make explicit the Pestov-Uhlmann range characterization of the geodesic X-ray transform, by constructing a basis of functions making up its range and co-kernel. Such a range characterization also t…

Tensor decomposition is an important technique for capturing the high-order interactions among multiway data. Multi-linear tensor composition methods, such as the Tucker decomposition and the CANDECOMP/PARAFAC (CP), assume that the complex interactions among objects are multi-linear, and are thus insufficient to repres…

New methods for scoring function decomposition improve forecast evaluation.

We introduce a variable importance measure to quantify the impact of individual input variables to a black box function. Our measure is based on the Shapley value from cooperative game theory. Many measures of variable importance operate by changing some predictor values with others held fixed, potentially creating unl…

This note contributes to the point calculus of persistent homology by extending Alexander duality to real-valued functions. Given a perfect Morse function $f: S^{n+1} \to [0,1]$ and a decomposition $S^{n+1} = U \cup V$ such that $M = \U \cap V$ is an $n$-manifold, we prove elementary relationships between the persisten…

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

New method for causal effect estimation with hidden confounders.