A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
The paper uncovers the mathematical structure enabling value decomposition in multi-agent systems.
problem Theoretical justification for why value decomposition works effectively in multi-agent systems remains underexplored.
method The paper introduces the concept of Markov entanglement to measure the underlying structure and demonstrates how it can be used to bound the decomposition error.
result The widely-used class of index policies is weakly entangled and enjoys a sublinear O(N) scale of decomposition error for N-agent systems.
A fast algorithm for generalized matrix regression improves machine learning performance.
problem Efficiently solving generalized matrix regression problems in machine learning.
method Utilizes sketching technique to achieve (1+ε) relative error with sketching sizes of order $\cO(ε^{-1/2})$.
result The Fast GMR algorithm achieves better performance in symmetric positive definite matrix approximation and single pass singular value decomposition.
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…
In this article, we derive a Bayesian model to learning the sparse and low rank PARAFAC decomposition for the observed tensor with missing values via the elastic net, with property to find the true rank and sparse factor matrix which is robust to the noise. We formulate efficient block coordinate descent algorithm and …
The paper analyzes error propagation in dynamic programming for stochastic control and option pricing.
problem Error propagation in dynamic programming for stochastic control and option pricing.
method Formulated a general dynamic programming framework, used RKHSs for nonparametric regression, and Monte Carlo subsampling for estimating continuation value.
result Proposed a rigorous error decomposition and control mechanism for error propagation in dynamic programming.
Researchers propose a new SSL risk decomposition method to evaluate and improve self-supervised learning models.
problem Self-supervised learning evaluation is limited to a single metric, providing little insight into model performance and improvement.
method Proposes an SSL risk decomposition that considers four error components: approximation, representation usability, probe generalization, and encoder generalization.
result Analysis of 169 SSL vision models reveals the main sources of error and provides insights for improving SSL models in specific settings.
The paper explores when and why value decomposition algorithms work in cooperative multi-agent reinforcement learning.
problem The applicability and convergence properties of value decomposition algorithms in cooperative multi-agent reinforcement learning are unclear.
method The paper introduces decomposable games and proves that applying the multi-agent fitted Q-Iteration algorithm leads to an optimal Q-function in these games.
result The paper offers theoretical insights into when and why value decomposition algorithms converge in cooperative multi-agent reinforcement learning.
This is a detailed tutorial paper which explains the Principal Component Analysis (PCA), Supervised PCA (SPCA), kernel PCA, and kernel SPCA. We start with projection, PCA with eigen-decomposition, PCA with one and multiple projection directions, properties of the projection matrix, reconstruction error minimization, an…
The paper proposes a principle for dynamically adjusting the granularity of reinforcement learning abstractions.
problem Lack of general principles for dynamically adjusting the granularity of reinforcement learning abstractions.
method The paper proposes a principle based on rate-distortion theory, formalized through a performance certificate decomposing value error into learning and abstraction error bounds.
result Soft state-action abstractions can achieve near-optimal performance under substantial lossy compression of state and action information.
New framework assesses value of labeled vs unlabeled data in latent variable models.
problem Determining the optimal use of labeled and unlabeled data in latent variable models.
method Developed a bias-variance decomposition of the generalization error for method-of-moments latent variable estimation, and introduced a correction for misspecification.
result Labeled data is more valuable than unlabeled data when models are misspecified, but this value can be reduced with correction.
In this paper, in following of the first part (which ADF tests using ACI evaluation) has conducted, Time Series (TSs) are analyzed using decomposition analysis. In fact, TSs are composed of four components including trend (long term behavior or progression of series), cyclic component (non-periodic fluctuation behavior…
Many modern big data applications feature large scale in both numbers of responses and predictors. Better statistical efficiency and scientific insights can be enabled by understanding the large-scale response-predictor association network structures via layers of sparse latent factors ranked by importance. Yet sparsit…
Bias - variance decomposition of the expected error defined for regression and classification problems is an important tool to study and compare different algorithms, to find the best areas for their application. Here the decomposition is introduced for the survival analysis problem. In our experiments, we study bias -…
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…
In the present paper, a decomposition formula for the call price due to Alòs is transformed into a Taylor type formula containing an infinite series with stochastic terms. The new decomposition may be considered as an alternative to the decomposition of the call price found in a recent paper of Alòs, Gatheral and Radoi…
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.
The paper bounds the mean absolute error in DNN vector-to-vector regression.
problem Bounding the mean absolute error in deep neural network based vector-to-vector regression.
method Error decomposition techniques in statistical learning theory and non-convex optimization theory were used to derive upper bounds for approximation, estimation, and optimization errors.
result Theoretical upper bounds for mean absolute error in DNN vector-to-vector regression were derived and validated experimentally.
The CUR matrix decomposition is an important extension of Nyström approximation to a general matrix. It approximates any data matrix in terms of a small number of its columns and rows. In this paper we propose a novel randomized CUR algorithm with an expected relative-error bound. The proposed algorithm has the advanta…
Low rank tensor decompositions are a powerful tool for learning generative models, and uniqueness results give them a significant advantage over matrix decomposition methods. However, tensors pose significant algorithmic challenges and tensors analogs of much of the matrix algebra toolkit are unlikely to exist because …
Paper tackles tensor decomposition for unaligned observations using RKHS and novel loss functions.
problem Tackles tensor decomposition for unaligned observations.
method Uses functions in RKHS to represent mode with unaligned observations, introduces versatile loss function, proposes optimization algorithm and stochastic gradient method.
result Demonstrates improved tensor decomposition efficiency and effectiveness with synthetic and real data.