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.
We discuss replica analytic continuation using several simple models in order to prove mathematically the validity of replica analysis, which is used in a wide range of fields related to large scale complex systems. While replica analysis consists of two analytical techniques, the replica trick (or replica analytic con…
The portfolio optimization problem in which the variances of the return rates of assets are not identical is analyzed in this paper using the methodology of statistical mechanical informatics, specifically, replica analysis. We define two characteristic quantities of an optimal portfolio, namely, minimal investment ris…
We analyse a linear regression problem with nonconvex regularization called smoothly clipped absolute deviation (SCAD) under an overcomplete Gaussian basis for Gaussian random data. We propose an approximate message passing (AMP) algorithm considering nonconvex regularization, namely SCAD-AMP, and analytically show tha…
In this paper, we use replica analysis to determine the investment strategy that can maximize the net present value for portfolios containing multiple development projects. Replica analysis was developed in statistical mechanical informatics and econophysics to evaluate disordered systems, and here we use it to formula…
Binary perceptron's instability linked to replica symmetry breaking.
The typical behavior of optimal solutions to portfolio optimization problems with absolute deviation and expected shortfall models using replica analysis was pioneeringly estimated by S. Ciliberti and M. Mézard [Eur. Phys. B. 57, 175 (2007)]; however, they have not yet developed an approximate derivation method for fin…
The paper estimates key metrics for linear models with Markov or hidden Markov sources.
This paper optimizes deep learning training by efficiently sharding weight updates across replicas.
We use variational Gaussian approximations to analyze parametric models with unknown data-generating distributions.
Previous studies into the budget constraint of portfolio optimization problems based on statistical mechanical informatics have not considered that the purchase cost per unit of each asset is distinct. Moreover, the fact that the optimal investment allocation differs depending on the size of investable funds has also b…
In this paper, we use replica analysis to investigate the influence of correlation among the return rates of assets on the solution of the portfolio optimization problem. We consider the behavior of the optimal solution for the case where the return rate is described with a single-factor model and compare the findings …
This study analyzes quantization in deep learning models using statistical physics methods.
New algorithm speeds up MCMC for deep learning models.
Dense Associative Memories outperform classical networks in robustness and signal processing.
In the present work, the optimal portfolio minimizing the investment risk with cost is discussed analytically, where this objective function is constructed in terms of two negative aspects of investment, the risk and cost. We note the mathematical similarity between the Hamiltonian in the mean-variance model and the Ha…
Replica exchange Langevin diffusion accelerates nonconvex optimization.
In this paper, as a first step in examining the properties of a feasible portfolio subset that is characterized by budget and risk constraints, we assess the maximum and minimum of the investment concentration using replica analysis. To do this, we apply an analytical approach of statistical mechanics. We note that the…
Improved reSGLD accelerates convergence in non-convex learning problems.
In the present paper, the primal-dual problem consisting of the investment risk minimization problem and the expected return maximization problem in the mean-variance model is discussed using replica analysis. As a natural extension of the investment risk minimization problem under only a budget constraint that we anal…
The Lasso performs well in ultra-sparse linear models with finite support size.
This research highlights the secrecy potential of nonlinear generative models and their all-or-nothing phase transition.
In the present work, eigenvalue distributions defined by a random rectangular matrix whose components are neither independently nor identically distributed are analyzed using replica analysis and belief propagation. In particular, we consider the case in which the components are independently but not identically distri…
SOCRATES uses LLMs to automate simulation optimization of complex systems.
Study dynamics of alternating minimization for bilinear regression under large system limits.
A fast, approximate method for variable selection in GLMs tackles correlated data.
Transfer learning improves prediction quality in high-dimensional sparse regression.
We rigorously prove statistical physics predictions for non-convex GLMs in high dimensions.
Proves formula for reconstruction performance in generalized linear models.
In this paper, we present a new practical method for Bayesian learning that can rapidly draw representative samples from complex posterior distributions with multiple isolated modes in the presence of mini-batch noise. This is achieved by simulating a collection of replicas in parallel with different temperatures and p…
In the present paper, the minimal investment risk for a portfolio optimization problem with imposed budget and investment concentration constraints is considered using replica analysis. Since the minimal investment risk is influenced by the investment concentration constraint (as well as the budget constraint), it is i…
PLS-SVD struggles with missing data in multimodal datasets, showing a phase transition in performance.
2D-PT improves sampling in constrained optimization problems.
BLADE uses Bayesian methods to discover complex systems from scarce data.
Deep networks preferentially learn shared features, avoiding memorization in early layers.
Derives asymptotic generalization error for large-margin classifiers.
Proposes r2SGLD for efficient constrained exploration in non-convex learning.
New sampler tackles complex discrete energy landscapes efficiently.
New method improves sparse signal reconstruction using 1RSB-AMP.
Statistical learning theory provides bounds of the generalization gap, using in particular the Vapnik-Chervonenkis dimension and the Rademacher complexity. An alternative approach, mainly studied in the statistical physics literature, is the study of generalization in simple synthetic-data models. Here we discuss the c…
Toy model study shows resampling/reweighting can improve feature learning in imbalanced classification.
Study binary perceptrons' capacity using random duality theory.
Study shows optimal self-distillation improves model performance on noisy data.
New method improves convergence and reduces variance in noisy optimization problems.
We investigate the signal reconstruction performance of sparse linear regression in the presence of noise when piecewise continuous nonconvex penalties are used. Among such penalties, we focus on the SCAD penalty. The contributions of this study are three-fold: We first present a theoretical analysis of a typical recon…
We analyze anomaly detection class imbalance using a solvable model.
Bayes-optimal limits in PCA with structured noise are determined.
We use a replica approach to deal with portfolio optimization problems. A given risk measure is minimized using empirical estimates of asset values correlations. We study the phase transition which happens when the time series is too short with respect to the size of the portfolio. We also study the noise sensitivity o…
We consider the problem of mean-variance portfolio optimization for a generic covariance matrix subject to the budget constraint and the constraint for the expected return, with the application of the replica method borrowed from the statistical physics of disordered systems. We find that the replica symmetry of the so…