The optimal binning is the optimal discretization of a variable into bins given a discrete or continuous numeric target. We present a rigorous and extensible mathematical programming formulation for solving the optimal binning problem for a binary, continuous and multi-class target type, incorporating constraints not p…
On-device research index
arXiv research
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.
168,695 papers · 148 categories
Trend · papers per month
48 results for “mathematical programming”
This paper reviews recent advances in the field of optimization under uncertainty via a modern data lens, highlights key research challenges and promise of data-driven optimization that organically integrates machine learning and mathematical programming for decision-making under uncertainty, and identifies potential r…
This paper studies dynamic stochastic optimization problems parametrized by a random variable. Such problems arise in many applications in operations research and mathematical finance. We give sufficient conditions for the existence of solutions and the absence of a duality gap. Our proof uses extended dynamic programm…
Mathematical model predicts international trade and global economy dynamics.
problem Understanding complex international trade and economy interactions.
method Developed a mathematical model for non-equilibrium processes in open systems.
result Predicted model accurately reflects international trade and economy.
This article is based upon lectures given at the 2013 IAS/Park City Mathematics Institute summer program in geometric analysis.
In this paper, we analyze dynamic programming as a novel approach to solve the problem of maximizing the profits of a bank. The mathematical model of the problem and the description of a bank's work is described in this paper. The problem is then approached using the method of dynamic programming. Dynamic programming m…
Defines a calculus for integrating Moreau envelopes in differentiable programming.
problem Lack of a mathematical framework for applying Moreau envelopes to deep networks and machine learning systems.
method Develops a compositional calculus adapted to Moreau envelopes and integrates it into differentiable programming.
result Integrates Moreau envelopes into differentiable programming, enabling new gradient back-propagation methods.
These lecture notes provide a self-contained introduction to the mathematical methods required in a Bachelor degree programme in Business, Economics, or Management. In particular, the topics covered comprise real-valued vector and matrix algebra, systems of linear algebraic equations, Leontief's stationary input-output…
Approximate dynamic programming is a popular method for solving large Markov decision processes. This paper describes a new class of approximate dynamic programming (ADP) methods- distributionally robust ADP-that address the curse of dimensionality by minimizing a pessimistic bound on the policy loss. This approach tur…
DisCoPyro combines category theory with machine learning for program learning.
problem Applying category theory to machine learning tasks.
method Introducing DisCoPyro, a framework combining categorical structures with amortized variational inference.
result DisCoPyro can be applied in program learning for variational autoencoders and potentially contributes to AGI.
Estimating a constrained relation is a fundamental problem in machine learning. Special cases are classification (the problem of estimating a map from a set of to-be-classified elements to a set of labels), clustering (the problem of estimating an equivalence relation on a set) and ranking (the problem of estimating a …
An article based on a four-lecture introductory minicourse on minimal surface theory given at the 2013 summer program of the Institute for Advanced Study and the Park City Mathematics Institute.
Mathematical study supports connection between 3D manifolds and modular tensor categories.
problem Connecting geometric topology and quantum topology using Chern-Simons invariants and Reidemeister torsions.
method Developed an algorithm to generate modular -matrices and quantum dimensions from Seifert fibered spaces and torus bundles over the circle.
result Mathematically constructed premodular categories from Seifert fibered spaces and torus bundles over the circle, conjecturing their modularity under specific conditions.
We describe an abstract control-theoretic framework in which the validity of the dynamic programming principle can be established in continuous time by a verification of a small number of structural properties. As an application we treat several cases of interest, most notably the lower-hedging and utility-maximization…
This work offers a broad perspective on probabilistic modeling and inference in light of recent advances in probabilistic programming, in which models are formally expressed in Turing-complete programming languages. We consider a typical workflow and how probabilistic programming languages can help to automate this wor…
Subset selection in multiple linear regression aims to choose a subset of candidate explanatory variables that tradeoff fitting error (explanatory power) and model complexity (number of variables selected). We build mathematical programming models for regression subset selection based on mean square and absolute errors…
The study evaluates how prediction helps identify the worst-off in welfare programs.
problem Identifying the most vulnerable individuals for support.
method Mathematical models and real-world case study on long-term unemployment.
result Prediction is more effective than other policy levers in surfacing the worst-off.
This paper proposes a general duality framework for the problem of minimizing a convex integral functional over a space of stochastic processes adapted to a given filtration. The framework unifies many well-known duality frameworks from operations research and mathematical finance. The unification allows the extension …
New method learns BN structures from data efficiently.
problem Learning sparse DAG structure of BN from continuous data.
method Consistent second-order conic integer programming with early stopping criterion.
result Near-optimal solutions to medium-size problems within reasonable time.
Hamiltonian Monte Carlo (HMC) is arguably the dominant statistical inference algorithm used in most popular "first-order differentiable" Probabilistic Programming Languages (PPLs). However, the fact that HMC uses derivative information causes complications when the target distribution is non-differentiable with respect…
New method uses dynamic programming for meta continual learning.
problem Challenges of generalization and catastrophic forgetting in sequential learning.
method Developed a theoretical framework using dynamic programming for meta continual learning.
result Theoretical and practical method achieves better accuracy than existing methods.
A Natural Copulaq-fin.RM
A new copula minimizes distance between distributions.
problem Arbitrariness in copula choice.
method Minimizes Wasserstein distance; linear programming estimation.
result Natural copula provides parsimonious estimation.
The paper proposes a happiness-based fairness framework using linear programming.
problem Fairness in decision-making outcomes.
method Linear programming to compute optimal, fair post-processing strategies.
result Unified and extended fairness definitions with practical strengths across diverse scenarios.
Develops a mathematical model for automatic differentiation in machine learning.
problem Current automatic differentiation lacks a simple mathematical model for machine learning.
method Articulates relationships between program differentiation and nonsmooth functions, provides a class of functions and nonsmooth calculus.
result Shows how nonsmooth calculus applies to stochastic approximation methods and evidence of artificial critical points.
We present the mathematical background of a software package that computes triangulations of mapping tori of surface homeomorphisms, suitable for Jeff Weeks's program SnapPea. It consists of two programs. jmt computes triangulations and prints them in a human-readable format. jsnap converts this format into SnapPea's t…
This survey was written for the Current Developments in Mathematics conference, 2012, and is an updating of my article "The Strominger-Yau-Zaslow conjecture: From torus fibrations to degenerations," in the Seattle 2005 proceedings. We trace progress and thinking about the SYZ conjecture since its introduction in 1996. …
The present article surveys some mathematical aspects of the BCOV holomorphic anomaly equations introduced by Bershadsky, Cecotti, Ooguri and Vafa. It grew from a series of lectures the authors gave at the Fields Institute in the Thematic Program of Calabi-Yau Varieties in the fall of 2013.
Algorithm selects variables and bandwidths for geographically weighted regression.
problem Estimating variable subsets and bandwidths for geographically weighted regression.
method Mathematical programming-based approach integrating variable selection and bandwidth estimation.
result Proposed algorithm provides stable spatially varying patterns with competitive explanatory power.
Zoetrope Genetic Programming improves symbolic regression performance.
problem Evolutionary symbolic regression for complex mathematical expressions.
method Zoetropic representation, repeated fusion operations, linear combination, crossover, mutation, selection.
result Zoetrope Genetic Programming achieves state-of-the-art performance and low computational time.
This paper describes a new method for Symbolic Regression that allows to find mathematical expressions from a dataset. This method has a strong mathematical basis. As opposed to other methods such as Genetic Programming, this method is deterministic, and does not involve the creation of a population of initial solution…
In (Franceschi et al., 2018) we proposed a unified mathematical framework, grounded on bilevel programming, that encompasses gradient-based hyperparameter optimization and meta-learning. We formulated an approximate version of the problem where the inner objective is solved iteratively, and gave sufficient conditions e…
On Experimentsstat.ML
Paper outlines a new mathematical language for experiments.
problem Formalizing the scientific process for automation.
method Formulates the scientific process in precise mathematical language.
result Novel contributions in data processing, bias variance, and deficiency.
Neural programming involves training neural networks to learn programs, mathematics, or logic from data. Previous works have failed to achieve good generalization performance, especially on problems and programs with high complexity or on large domains. This is because they mostly rely either on black-box function eval…
Richard Bellman's Principle of Optimality, formulated in 1957, is the heart of dynamic programming, the mathematical discipline which studies the optimal solution of multi-period decision problems. In this paper, we look at the main trading principles of Jesse Livermore, the legendary stock operator whose method was pu…
ParaDRAM automates parallel MCMC simulations across languages.
problem Efficiently sampling complex mathematical functions.
method Automated, parallel, high-performance MCMC with adaptive rejection.
result Significant memory reduction for complex simulations.
The SCMU algorithm computes cone factorizations for symmetric cones, improving upon existing methods.
problem Computing cone factorizations for symmetric cones in optimization.
method Introduces and analyzes the symmetric-cone multiplicative update (SCMU) algorithm.
result The SCMU algorithm non-decreases the squared loss objective.
Reasoning models generate differently based on problem difficulty, not just length.
problem Understanding how reasoning models handle different problem difficulties.
method Examined hidden-state trajectories across competitive programming, mathematics, and Boolean satisfiability.
result Corrected trajectory geometry shows difficulty-dependent differences in reasoning models, with stronger effects in the code domain.
Choosing a portfolio of risky assets over time that maximizes the expected return at the same time as it minimizes portfolio risk is a classical problem in Mathematical Finance and is referred to as the dynamic Markowitz problem (when the risk is measured by variance) or more generally, the dynamic mean-risk problem. I…
In this study we introduce a new technique for symbolic regression that guarantees global optimality. This is achieved by formulating a mixed integer non-linear program (MINLP) whose solution is a symbolic mathematical expression of minimum complexity that explains the observations. We demonstrate our approach by redis…
These are lecture notes from the Clay Mathematics Institute summer school ``Floer Homology, Gauge Theory, and Low Dimensional Topology'' Alfred Renyi Institute; www.claymath.org/programs/summer_school/2004/. The main goal of these notes is to sketch a proof of Giroux correspondence between open book decompositions of t…
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.
In mathematics, a knot is a single strand of string crossed over itself any number of times, and connected at the ends. The Reidemeister Moves have been proven to be the three core moves necessary to fully untangle a knot. Some knots can be untangled to a loop (the unknot), while others are fundamentally knotted. We de…
Novel approach trains LLMs for inductive reasoning using probabilistic programs.
problem Training LLMs for inductive reasoning with sparse, ambiguous data.
method Program-based Posterior Training (PPT) using probabilistic inference.
result Significant improvement in estimation accuracy and alignment with human judgments.
The paper optimizes portfolios in a market with hidden drift and random expert opinions.
problem Optimizing portfolios in a market with hidden Gaussian drift and random expert signals.
method Modeling the hidden drift using Kalman filters and solving the utility maximization problem with dynamic programming.
result Derivation of optimal portfolio weights and utility maximization under the given market conditions.
Learning directed acyclic graphs (DAGs) from data is a challenging task both in theory and in practice, because the number of possible DAGs scales superexponentially with the number of nodes. In this paper, we study the problem of learning an optimal DAG from continuous observational data. We cast this problem in the f…
We solve the problem of optimal stopping of a Brownian motion subject to the constraint that the stopping time's distribution is a given measure consisting of finitely-many atoms. In particular, we show that this problem can be converted to a finite sequence of state-constrained optimal control problems with additional…
The analysis of markets with indivisible goods and fixed exogenous prices has played an important role in economic models, especially in relation to wage rigidity and unemployment. This research report provides a mathematical and computational details associated to the mathematical programming based approaches proposed…
Graph clustering improved using Boltzmann machine heuristics.
problem Graph clustering to form densely connected clusters.
method Two mathematical programming formulations, two variations of Boltzmann machine heuristic.
result Boltzmann machine provides superior solutions and faster computation times.