OKRidge solves sparse ridge regression problems for nonlinear systems.
problem Identifying sparse governing equations for nonlinear dynamical systems.
method OKRidge algorithm using saddle point formulation and ADMM-based approach with efficient proximal operators.
result OKRidge achieves provable optimality with significantly faster run times than Gurobi.
Unified framework for sparse logistic regression with nonconvex regularization.
problem Sparse logistic regression with nonconvex regularization.
method Unified framework, line search criteria for nonconvex terms.
result Effective classification and feature selection at lower computational cost.
SGD improves DR by solving two-stage sampling problems.
problem Improving the learning properties of SGD for distribution regression.
method Applying SGD to two-stage sampling problems in distribution regression.
result Theoretical guarantees for SGD's performance in DR, with optimal bounds.
AM converges super-linearly for solving mixed linear regression problems.
problem Learning linear regressors from unlabeled observations in multiple linear regression models.
method Alternating Minimization (AM) algorithm, which alternates between label estimation and regression solving.
result AM converges super-linearly in certain parameter regimes, requiring only O(log log(1/ε)) iterations to achieve an error of ε.
Two methods solve kernel ridge regression problems efficiently.
problem Solving kernel ridge regression problems with large datasets.
method RPCholesky and KRILL preconditioning techniques.
result Efficient solutions to KRR problems with strong guarantees.
Solving logistic regression with L1-regularization in distributed settings is an important problem. This problem arises when training dataset is very large and cannot fit the memory of a single machine. We present d-GLMNET, a new algorithm solving logistic regression with L1-regularization in the distributed settings. …
Randomized algorithm solves vector-valued regression problems with low-rank operators.
problem Vector-valued regression problems involving infinite-dimensional spaces.
method Randomized Reduced Rank Regression (R4) using Gaussian sketching for optimization.
result R4 estimators are efficient and accurate, with empirical risk close to optimal.
A new screening rule speeds up OWL regression solving.
problem High-dimensional sparse learning with OWL regression's computational cost and memory usage.
method Safe screening rule for OWL regression using iterative strategy.
result Significant computational gain without accuracy loss.
Proposes mutual information for regression without prior knowledge.
problem Regression tasks without prior model knowledge.
method Mutual information learning formulation, SGD convergence analysis.
result High dimensionality can be beneficial with a threshold.
We present a novel binary convex reformulation of the sparse regression problem that constitutes a new duality perspective. We devise a new cutting plane method and provide evidence that it can solve to provable optimality the sparse regression problem for sample sizes n and number of regressors p in the 100,000s, that…
New algorithms solve large-scale convex regression problems.
problem Large-scale convex regression with subgradient regularization.
method Active set type algorithm on dual QP, approximate optimization, randomized augmentation.
result Solves problems with n=10^5 and d=10 in minutes.
Paper introduces methods to create fair and accurate regression models.
problem Creating fair and accurate regression models.
method Mixed-integer optimization methods, exact formulations, branch-and-bound algorithm, coordinate descent algorithm.
result Developed methods produce fair and accurate models with reduced training times.
Transformer attention layers solve single-location regression tasks.
problem Understanding token-wise sparsity and internal linear representations in attention-based models.
method Introduce single-location regression task and a simplified predictor based on self-attention layers.
result Transformer attention layers are asymptotically Bayes optimal and can learn underlying structures effectively.
Develops state-space deep Gaussian processes for irregular signals.
problem Solving deep Gaussian process regression problems for irregular signals/functions.
method Represent DGPs as SDEs, solve using state-space filtering and smoothing methods.
result Rich class of priors compatible with irregular signals/functions.
PIANO speeds up multinomial logistic regression solving.
problem Handling large datasets and many classes in logistic regression.
method Parallel iterative algorithm based on Majorization Minimization.
result PIANO converges to a stationary point of Multinomial and Sparse Multinomial Logistic Regression.
A new data-oblivious sketch for logistic regression reduces data size while maintaining approximation accuracy.
problem Efficiently solving logistic regression in one pass over a data stream.
method Data-oblivious sketching approach that reduces data size to poly(μdlog n) weighted points.
result Sketching reduces data size significantly and provides approximation guarantees.
A new screening rule improves lasso solving speed.
problem Efficiently solving lasso problems with high correlation.
method Uses second-order information from the Hessian to screen predictors.
result Outperforms alternatives on simulated and real data.
In kernel methods, the kernels are often required to be positive definite, which restricts the use of many indefinite kernels. To consider those non-positive definite kernels, in this paper, we aim to build an indefinite kernel learning framework for kernel logistic regression. The proposed indefinite kernel logistic r…
PARC uses piecewise linear predictors for regression and classification.
problem Multivariate regression and classification problems.
method Alternates between ridge and softmax regression, and cluster assignment based on accuracy and separability.
result Converges to a local minimum in a finite number of steps.
Regression trees learn gradients of differentiable functions.
problem Understanding gradients of differentiable functions using regression trees.
method Developed a method to estimate gradients of differentiable functions using regression trees and exposed quantities from tree learning libraries.
result Gradient estimates from regression trees can be used to improve predictive analysis and solve tasks in uncertainty quantification.
Novel probabilistic solver speeds up solving related linear systems.
problem Efficiently solving multiple related linear systems.
method Probabilistic linear solver over the parameter space, leveraging solved systems.
result Faster and more efficient solution of related linear systems.
Extends RRR to capture nonlinear interactions in multi-response regression.
problem Complex relationships in real-world data cannot be adequately modeled by linear interactions.
method Introduces Higher Order Reduced Rank Regression (HORRR) using tensor representations and Tucker decomposition.
result HORRR can capture nonlinear interactions in multi-response regression.
Solves weakly supervised regression using low-rank approximations and manifold regularization.
problem Weakly supervised regression with known, unknown, and uncertain labels.
method Combines manifold regularization and low-rank matrix decomposition for optimization.
result Improves solution quality and stability for large datasets.
TensorSketch is an oblivious linear sketch introduced in Pagh'13 and later used in Pham, Pagh'13 in the context of SVMs for polynomial kernels. It was shown in Avron, Nguyen, Woodruff'14 that TensorSketch provides a subspace embedding, and therefore can be used for canonical correlation analysis, low rank approximation…
FasTR efficiently solves sparse and unit-rank tensor regression problems.
problem Sparse and unit-rank tensor regression problems in tensor data analysis.
method FasTR decomposes tensor coefficients into component vectors and estimates each with ℓ1 regularized regression, solving in parallel. result FasTR computes better solutions faster than baseline models.
Proposes a new method to improve regression models with reweighted samples.
problem Improves regression models' performance under low sample sizes and covariate perturbations.
method Reparametrizes sample weights using a doubly non-negative matrix and solves the reweighted estimate efficiently.
result Adversarial reweighting strategy delivers promising results on various datasets.
The l1-regularized logistic regression (or sparse logistic regression) is a widely used method for simultaneous classification and feature selection. Although many recent efforts have been devoted to its efficient implementation, its application to high dimensional data still poses significant challenges. In this paper…
Paper solves NP-hard sparse mixed linear regression problem with provable guarantees.
problem Sparse mixed linear regression on unlabeled data.
method Invex relaxation for intractable problem with theoretical guarantees.
result Exact recovery of data labels and close approximation of regression parameters.
Proposes SHORE model for efficient MOR with sparsity and scalability.
problem Challenges of interpretability and scalability in MOR with high-dimensional outputs.
method Incorporates sparsity requirements and a two-stage optimization framework for efficient compression.
result Theoretical and empirical validation of the proposed framework's efficiency and accuracy.
Flexible empirical Bayes for large-scale multiple linear regression.
problem Large-scale multiple linear regression with flexible priors and efficient computation.
method Adaptive shrinkage priors combined with variational approximations for hyperparameter estimation.
result The posterior mean from the empirical Bayes method solves a penalized regression problem.
Private sketches protect linear regression data privacy.
problem Protecting sensitive information in linear regression.
method Release private sketches of datasets, compute approximate solutions.
result Private sketches maintain good approximation guarantees to the original problem.
We propose to solve a label ranking problem as a structured output regression task. We adopt a least square surrogate loss approach that solves a supervised learning problem in two steps: the regression step in a well-chosen feature space and the pre-image step. We use specific feature maps/embeddings for ranking data,…
In this note we propose a new approach towards solving numerically optimal stopping problems via reinforced regression based Monte Carlo algorithms. The main idea of the method is to reinforce standard linear regression algorithms in each backward induction step by adding new basis functions based on previously estimat…
Paper studies how few pretraining tasks are needed for a linear model to solve new tasks.
problem How many pretraining tasks are needed for a linear model to solve new tasks?
method Pretrained a linear attention model for linear regression with a Gaussian prior.
result Effective pretraining requires a small number of independent tasks, and the model closely matches Bayes optimal.
New algorithm solves ℓ0-norm constrained multilinear logistic regression for tensor data.
problem Non-convex and nonsmooth ℓ0-norm constraints in multilinear logistic regression. method APALM+ method for globally convergent optimization. result APALM+ ensures convergence to a first-order critical point. The least squares Monte Carlo algorithm has become popular for solving portfolio optimization problems. A simple approach is to approximate the value functions on a discrete grid of portfolio weights, then use control regression to generalize the discrete estimates. However, the classical global control regression can …
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.
New insights into statistical and computational limits for mixed sparse linear regression.
problem Recovering two sparse signals from noisy linear measurements.
method Analysis of low-degree polynomials and a simple thresholding algorithm.
result Identification of a smooth information-computation tradeoff and order-optimality of the thresholding algorithm.
Big T-Rex solves FDR-controlled sparse regression on laptops with millions of variables.
problem Scalable FDR-controlled variable selection for high-dimensional data.
method Early terminated random experiments with memory-mapping and permutation-based dummy generation.
result Solves FDR-controlled Lasso problems with 5 million variables on a laptop in 30 minutes.
This paper uses quantum computing to solve sparse linear regression problems efficiently.
problem Sparse linear regression to identify important features from a large set of variables.
method Formulates the ℓ0 optimization problem as a QUBO problem and solves it using the D-Wave adiabatic quantum computer. result The QUBO solution matches the optimal solution for a wide range of sparsity penalty values across datasets.
Machine learning models solve inverse eigenvalue problems for symmetric potentials and refractive indices.
problem Solving inverse eigenvalue problems for symmetric potentials and refractive indices.
method Supervised regression models (k-Nearest Neighbours, Random Forests, Multi-Layer Perceptron) trained on eigenvalue datasets.
result Machine learning methods can numerically solve inverse eigenvalue problems under appropriate parameter tuning.
Regression is widely used by practioners across many disciplines. We reformulate the underlying optimisation problem as a second-order conic program providing the flexibility often needed in applications. Using examples from portfolio management and quantitative trading we solve regression problems with and without con…
Introduces PPMM algorithm for nonconvex robust regression problems.
problem Nonconvex tuning-free robust regression problems.
method PPMM algorithm with inner subproblems solved by SSN-PPA.
result Converges to d-stationary point with KL property.
Efficiently solves inverse classification problems for logistic and softmax models.
problem Finding instances that change classifier predictions.
method Closed-form solution for logistic regression, iterative optimization for softmax.
result Fast, exact solutions for high-dimensional instances and many classes.
Develops a regression approach for solving MDPs with general state and action spaces.
problem Solving MDPs with large or infinite state and action spaces.
method Regression-based primal-dual martingale approach.
result Tight upper and lower approximations of value functions and optimal policies.
Wasserstein framework solves mixed linear regression problems.
problem Mixed linear regression with multi-modal distributions.
method Wasserstein distance minimization for nonconvex-concave minimax optimization.
result WMLR achieves global convergence and generalization guarantees for two linear models.
We propose a data aggregation-based algorithm with monotonic convergence to a global optimum for a generalized version of the L1-norm error fitting model with an assumption of the fitting function. The proposed algorithm generalizes the recent algorithm in the literature, aggregate and iterative disaggregate (AID), whi…
We give improved algorithms for the ℓp-regression problem, minx∥x∥p such that Ax=b, for all p∈(1,2)∪(2,∞). Our algorithms obtain a high accuracy solution in O~p(m2p+∣p−2∣∣p−2∣)≤O~p(m31) iterations, where each iteration requires s…