We describe dimensionally constrained symbolic regression which has been developed for mass measurement in certain classes of events in high-energy physics (HEP). With symbolic regression, we can derive equations that are well known in HEP. However, in problems with large number of variables, we find that by constraini…
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48 results for “constrained regression”
We find the optimal error for a constrained regression model under a linear model.
problem Minimizing error while adhering to demographic parity constraints.
method Proposed a minimax optimal error analysis for a demographic parity-constrained regression problem within a linear model.
result The minimax optimal error is characterized by $Θ( rac{dM}{n})$.
Shape-constrained symbolic regression improves model extrapolation with prior knowledge.
problem Improving model extrapolation with prior knowledge in symbolic regression.
method Shape-constrained symbolic regression using evolutionary algorithms with interval arithmetic.
result Models with shape constraints have improved extrapolation but lower accuracy on test sets.
Learning with Physical Constraintsphysics.flu-dyn
Three physics-constrained regression exercises for image velocimetry and turbulence modeling.
problem Image velocimetry and turbulence modeling challenges.
method Physics-constrained regression exercises implemented as toy problems.
result Python codes provided for all exercises.
Paper tackles multivariate shape-constrained convex regression problems.
problem Fitting a convex function to data with component-wise monotonicity and uniform Lipschitz continuity.
method Least squares estimator via solving a constrained convex quadratic programming problem. Efficient algorithms designed: sGS-ADMM and pALM.
result Both proposed algorithms outperform state-of-the-art methods in numerical experiments.
This article reviews and explains HMC-based methods for sampling constrained continuous distributions.
problem Sampling from continuous distributions with constraints.
method HMC and related methods for constrained sampling.
result HMC and related methods are more efficient for constrained sampling.
Cactus improves auto-regressive decoding speed without sacrificing quality.
problem Accelerating auto-regressive decoding while maintaining output quality.
method Formalizes speculative sampling as constrained optimization and proposes Cactus for controlled divergence from the verifier distribution.
result Empirically validated effectiveness across various benchmarks.
Approximation bounds for norm constrained neural networks with applications to regression and GANscs.LG
The paper bounds neural networks' approximation error and applies it to regression and GANs.
problem Bounding the approximation error of norm-constrained neural networks.
method Proved upper and lower bounds on approximation error using Rademacher complexity.
result Obtained convergence rates for over-parameterized neural networks and optimal GAN learning rates.
Functional BART with Shape Priors: A Bayesian Tree Approach to Constrained Functional Regressionstat.ME
Functional BART adds shape priors to Bayesian tree regression for better curve fitting.
problem Regression with function-on-scalar data and shape constraints.
method Bayesian tree structure with spline representations, customized Bayesian backfitting algorithm, shape priors.
result Improved estimation and prediction accuracy with shape priors.
Optimizes binary regression models with gradient ascent-descent methods.
problem Regression problems with binary weights in quantized learning and digital communication.
method Maximin optimization using gradient ascent-descent methods.
result The approach is optimal in linear regression with low noise and robust regression with few outliers.
The paper analyzes constrained optimal portfolios in high dimensions using novel statistical learning techniques.
problem Forming optimal portfolios with constraints in high-dimensional asset spaces.
method CROWN method integrating factor models with nodewise regression for estimation in large dimensions.
result Demonstrates estimation consistency and convergence rates for constrained portfolio weights, risk, and Sharpe Ratio.
The linear regression problem is to minimize over , where , , and . To avoid overfitting and bound , the constrained regression minimizes over every unit vector . This makes the pr…
Statistical models with constrained probability distributions are abundant in machine learning. Some examples include regression models with norm constraints (e.g., Lasso), probit, many copula models, and latent Dirichlet allocation (LDA). Bayesian inference involving probability distributions confined to constrained d…
We investigate Monte Carlo based algorithms for solving stochastic control problems with probabilistic constraints. Our motivation comes from microgrid management, where the controller tries to optimally dispatch a diesel generator while maintaining low probability of blackouts. The key question we investigate are empi…
Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fieldsphysics.flu-dyn
Paper develops physics-informed, boundary-constrained Gaussian process for fluid flow field reconstruction.
problem Reconstructing fluid flow fields from limited data.
method Physics-informed, boundary-constrained Gaussian process regression.
result Derives physics-informed kernels for simulating incompressible flows.
The paper improves GP regression for sparse sensor data in structural mode shape reconstruction.
problem Reconstructing full-field structural mode shapes from sparse sensor data.
method Physics-Constrained Single-Output Gaussian Process (CONS-SOGP) framework.
result The proposed method provides more accurate and reliable mode shapes.
Regularization aims to improve prediction performance of a given statistical modeling approach by moving to a second approach which achieves worse training error but is expected to have fewer degrees of freedom, i.e., better agreement between training and prediction error. We show here, however, that this expected beha…
Gaussian processes (GPs) provide a powerful framework for extrapolation, interpolation, and noise removal in regression and classification. This paper considers constraining GPs to arbitrarily-shaped domains with boundary conditions. We solve a Fourier-like generalised harmonic feature representation of the GP prior in…
Scalable algorithms to solve optimization and regression tasks even approximately, are needed to work with large datasets. In this paper we study efficient techniques from matrix sketching to solve a variety of convex constrained regression problems. We adopt "Iterative Hessian Sketching" (IHS) and show that the fast C…
New sparse Gaussian process method tackles unconstrained regression problems.
problem Dealing with physical systems that satisfy inequality constraints.
method Extends constrained Gaussian process by redefining hat basis functions.
result Reduces computational complexity from to .
Group fairness is an important concern for machine learning researchers, developers, and regulators. However, the strictness to which models must be constrained to be considered fair is still under debate. The focus of this work is on constraining the expected outcome of subpopulations in kernel regression and, in part…
Proposes a new Lasso method with performance constraints.
problem No control over prediction accuracy for certain individuals.
method Adds quadratic performance constraints to Lasso-based objective functions.
result Defines a constrained sparse regression model through nonlinear optimization.
New algorithms improve sampling from constrained distributions.
problem Generating samples from distributions under constraints.
method Kinetic Langevin dynamics and splitting schemes.
result Improved complexity bounds over existing methods.
Novel method uses Gaussian process to estimate particle sizes from scattering data.
problem Estimating particle size distributions from noisy optical scattering measurements.
method Constrained Gaussian process regression with normalization constraints.
result Accurately reconstructs particle size distributions from noisy data.
Support vector regression (SVR) is one of the most popular machine learning algorithms aiming to generate the optimal regression curve through maximizing the minimal margin of selected training samples, i.e., support vectors. Recent researchers reveal that maximizing the margin distribution of whole training dataset ra…
c-lasso is a Python tool for robust and sparse regression with linear constraints.
problem Sparse and robust linear regression with linear constraints.
method Estimates coefficients and scale under linear constraints using perspective M-estimators.
result Provides estimators for various loss functions with linear constraints.
In this paper we explore different regression models based on Clusterwise Linear Regression (CLR). CLR aims to find the partition of the data into clusters, such that linear regressions fitted to each of the clusters minimize overall mean squared error on the whole data. The main obstacle preventing to use found re…
Many DNN-enabled vision applications constantly operate under severe energy constraints such as unmanned aerial vehicles, Augmented Reality headsets, and smartphones. Designing DNNs that can meet a stringent energy budget is becoming increasingly important. This paper proposes ECC, a framework that compresses DNNs to m…
Sparsity-constrained optimization has wide applicability in machine learning, statistics, and signal processing problems such as feature selection and compressive Sensing. A vast body of work has studied the sparsity-constrained optimization from theoretical, algorithmic, and application aspects in the context of spars…
Finite mixtures of regression models offer a flexible framework for investigating heterogeneity in data with functional dependencies. These models can be conveniently used for unsupervised learning on data with clear regression relationships. We extend such models by imposing an eigen-decomposition on the multivariate …
Proposes a Gaussian process model for constrained dynamics learning.
problem Challenges in identifying constrained dynamics of mechanical systems.
method Combines analytical mechanics with Gaussian process regression.
result Improves data efficiency and constraint integrity in predictions.
In this paper, we revisit the large-scale constrained linear regression problem and propose faster methods based on some recent developments in sketching and optimization. Our algorithms combine (accelerated) mini-batch SGD with a new method called two-step preconditioning to achieve an approximate solution with a time…
The study establishes risk bounds for distributional regression estimators.
problem Estimating distributional regression models with nonparametric methods.
method Theoretical bounds for CRPS and MSE are derived for convex and non-convex constraints.
result Theoretical risk bounds are validated through experiments on simulated and real data.
Logistic regression gets a new, simpler uniform bound.
problem Finding a uniform bound for logistic regression's empirical risk.
method PAC-Bayes approach with second-order expansion and Rademacher-complexity bounds.
result Provides a dimension-free uniform concentration bound.
Meta-theorems validate fair regression algorithms under demographic parity constraints.
problem Regression under demographic parity constraints.
method Meta-theorems and post-processing methods.
result Fair minimax optimal regression can be achieved through post-processing.
We consider the problem of nonparametric regression under shape constraints. The main examples include isotonic regression (with respect to any partial order), unimodal/convex regression, additive shape-restricted regression, and constrained single index model. We review some of the theoretical properties of the least …
ICCNLS models complex relationships as convex and concave components.
problem Complex input-output relationships with affine ambiguity.
method Sub-gradient constrained affine functions, global orthogonality constraints, L1, L2, and elastic net regularisation.
result Improved predictive accuracy and model simplicity compared to conventional methods.
Collider regression improves predictive performance in regression tasks.
problem Discarding prior causal knowledge in regression tasks.
method Collider regression framework incorporating probabilistic causal knowledge from collider structures.
result Proves positive generalization benefit and provides closed-form estimators.
New methods reduce computational cost for Gaussian Markov Random Fields with sparse constraints.
problem Inference and simulation of GMRFs are computationally prohibitive with many constraints.
method Proposes a basis transformation into blocks of constrained and non-constrained subspaces.
result Significantly outperforms existing alternatives in computational cost.
Machine learning models predict brain age with systematic bias, corrected in this study.
problem Systematic bias in machine learning regression models for brain age prediction.
method General constrained optimization approach to correct bias.
result Our method effectively eliminates the bias from brain age predictions.
New method improves robustness of neural network-based debiasing.
problem Improving robustness of neural network-based debiasing.
method Moment-constrained learning for neural networks.
result Improved performance compared to state-of-the-art benchmarks.
The paper develops methods for time-varying constrained online convex optimization.
problem Time-varying loss and constraint functions in online convex optimization.
method Model-based augmented Lagrangian methods (MALM) for time-varying and delayed feedback.
result Sublinear regret and constraint violation for both time-varying and delayed feedback scenarios.
On best subset regressionstat.ME
In this paper we discuss the variable selection method from \ell0-norm constrained regression, which is equivalent to the problem of finding the best subset of a fixed size. Our study focuses on two aspects, consistency and computation. We prove that the sparse estimator from such a method can retain all of the importa…
KL-constrained API shows optimization issues and improved with regularization.
problem Optimization issues in KL-constrained API algorithms.
method Comparison of KL divergence as a constraint vs. regularizer, empirical evaluation.
result KL-constrained API is not guaranteed to converge and incurs linear regret.
We present pairwise fairness metrics for ranking models and regression models that form analogues of statistical fairness notions such as equal opportunity, equal accuracy, and statistical parity. Our pairwise formulation supports both discrete protected groups, and continuous protected attributes. We show that the res…
New algorithms optimize constrained problems faster, avoiding full set optimization.
problem Optimizing constrained problems efficiently and quickly.
method Designing accelerated first-order algorithms that avoid full set optimization.
result Proved convergence to stationary points in nonconvex settings and accelerated rates in convex settings.
Paper tackles distributed linear regression with compositional covariates.
problem Solving distributed statistical methodology and computing for massive compositional data.
method Proposes two distributed optimization techniques based on ADMM and CDMM for solving constrained convex optimization problems.
result Established convergence theories for the proposed algorithms under regularity conditions.
New method solves constrained self-concordant minimization problems efficiently.
problem Constrained self-concordant minimization problems.
method Newton Frank-Wolfe method using linear minimization oracles.
result The method uses nearly the same number of linear minimization calls as the Frank-Wolfe method.