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…
Replica exchange Langevin diffusion accelerates nonconvex optimization.
A fast, approximate method for variable selection in GLMs tackles correlated data.
Dense Associative Memories outperform classical networks in robustness and signal processing.
SOCRATES uses LLMs to automate simulation optimization of complex systems.
We use variational Gaussian approximations to analyze parametric models with unknown data-generating distributions.
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…
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…
The paper estimates key metrics for linear models with Markov or hidden Markov sources.
New algorithm speeds up MCMC for deep learning models.
BLADE uses Bayesian methods to discover complex systems from scarce data.
This paper optimizes deep learning training by efficiently sharding weight updates across replicas.
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…
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…
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…
2D-PT improves sampling in constrained optimization problems.
Binary perceptron's instability linked to replica symmetry breaking.
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 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…
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.
Study binary perceptrons' capacity using random duality theory.
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…
New method improves convergence and reduces variance in noisy optimization problems.
This research highlights the secrecy potential of nonlinear generative models and their all-or-nothing phase transition.
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…
ADA augments data using AR replicas for robust regression.
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…
Proves formula for reconstruction performance in generalized linear models.
Proposes r2SGLD for efficient constrained exploration in non-convex learning.
Study dynamics of alternating minimization for bilinear regression under large system limits.
Statistical physics helps solve complex machine learning problems.
New sampler tackles complex discrete energy landscapes efficiently.
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…
Improved reSGLD accelerates convergence in non-convex learning problems.
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…
We study high-dimensional Gaussian mixture classification using statistical physics methods.
Paper discusses prediction errors for penalized regressions using GAMP and LOOCV.
This work improves autonomous racing by creating diverse opponents and adapting risk.
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 study improves the perceptron's storage capacity by optimizing variable selection.
Statistical physics approaches can be used to derive accurate predictions for the performance of inference methods learning from potentially noisy data, as quantified by the learning curve defined as the average error versus number of training examples. We analyse a challenging problem in the area of non-parametric inf…
Paper introduces supervised and unsupervised TAM models for binary neurons.
Study on signal recovery from low-rank matrix with sparse noise.
Toy model study shows resampling/reweighting can improve feature learning in imbalanced classification.
We rigorously prove statistical physics predictions for non-convex GLMs in high dimensions.
Derives asymptotic generalization error for large-margin classifiers.
We describe parallel Markov chain Monte Carlo methods that propagate a collective ensemble of paths, with local covariance information calculated from neighboring replicas. The use of collective dynamics eliminates multiplicative noise and stabilizes the dynamics thus providing a practical approach to difficult anisotr…