This paper studies robust regression in the settings of Huber's -contamination models. We consider estimators that are maximizers of multivariate regression depth functions. These estimators are shown to achieve minimax rates in the settings of -contamination models for various regression problems including nonpa…
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48 results for “functional linear regression”
We simplify complex regression coefficients using linearization and feature comparison.
problem Interpreting high-dimensional regression coefficients from nonlinear responses.
method Developed a linearization method to derive feature coefficients and compare them with regression coefficients.
result Shows how regression coefficients relate to linearized feature coefficients and how they change under regularization.
New method uses DC functions for piecewise linear regression.
problem Regression with piecewise linear constraints.
method Estimates piecewise linear convex functions using a difference of convex functions.
result Method achieves close to minimax statistical risk and comparable performance to existing methods.
Paper analyzes agnostic learning of mixed linear regression without generative models.
problem Learning mixed linear regression without assuming stochastic generation.
method Expectation Maximization (EM) and Alternating Minimization (AM) algorithms.
result AM and EM algorithms converge to population loss minimizers under standard conditions.
An analysis of linear regression and neural networks approximation for the pricing of swing optionsq-fin.MF
This paper compares linear regression and neural networks for pricing swing options.
problem Pricing swing options using approximation methods.
method Linear regression and neural networks for approximating the continuation value and swing price.
result The approximation methods converge to the actual swing price as the number of functions or Monte Carlo samples increases.
This paper analyzes divide-and-conquer estimators for functional linear regression without assuming target function in the RKHS.
problem Functional linear regression without target function in RKHS.
method Integral operator approach to establish upper bounds and prove asymptotic optimality.
result Sharp finite sample upper bounds and asymptotic optimality of divide-and-conquer estimators.
New GP model estimates piecewise continuous functions.
problem Piecewise continuous regression functions in scientific and engineering applications.
method Local Gaussian process model with partitioned local data and joint estimation of boundaries.
result Superior performance over conventional GP models in estimating piecewise regression functions.
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.
Brenier Isotonic Regressionstat.ML
Brenier isotonic regression extends multi-output isotonic regression using optimal transport.
problem Enforcing cyclic monotonicity in multi-output regression.
method Leverage Kantorovich's optimal transport to find cyclically monotone couplings.
result Brenier isotonic regression outperforms baselines in probability calibration.
Proposes a new model for non-linear regression of multivariate time series data.
problem Regression models for non-scalar variables, especially time series, have limitations.
method Develops a non-linear function-on-function model using neural networks.
result Demonstrates effectiveness through real-world applications.
Proposes adaptive ridge regression for functional linear models with piecewise shapes.
problem Functional linear regression with unknown coefficient function.
method Adaptive piecewise function template with penalization.
result Improves predictive power and interpretability compared to standard methods.
Two-Point Deterministic Equivalence for Stochastic Gradient Dynamics in Linear Modelscond-mat.dis-nn
Unified derivation of high-dimensional linear models using stochastic gradient descent.
problem Performance analysis of high-dimensional linear models trained with stochastic gradient descent.
method Derivation of a deterministic equivalence for the two-point function of a random matrix resolvent.
result Unified understanding of model performance including previously known and novel results.
Paper presents a machine learning method to improve significance tests for misspecified linear models.
problem Misspecification of linear assumptions in social science models leads to inaccurate significance levels.
method Apply machine learning to fit ground truth function, calculate linear approximation, and adjust the estimator.
result The method significantly outperforms linear regression for non-linear ground truth functions.
Generalisation and benign over-fitting for linear regression onto random functional covariatesstat.ML
Study predictive performance of linear regression with random functional covariates.
problem Theoretical predictive performance of linear regression with random functional covariates.
method Theoretical analysis of ridge and ridge-less least-squares regression with random functional covariates.
result Probabilistic bounds on predictive excess risk for random functional covariates.
New neural network models for complex functional data analysis.
problem Complex relations between functional predictors and responses.
method Function-on-Function regression models using neural networks with continuous hidden layers.
result Demonstrated power and flexibility in handling complex functional models.
Paper presents ABGD for efficient piecewise linear regression in high dimensions.
problem Efficiently solving piecewise linear regression in high-dimensional spaces.
method Parametrizes piecewise linear functions as difference of max-affine functions, using ABGD algorithm.
result ABGD converges linearly to an ε-accurate estimate with optimal sample complexity.
Optimal sketching bounds for sparse linear regression under various loss functions are established.
problem Sparse linear regression under different loss functions.
method Distribution over oblivious sketches for sparse norm regression and hinge-like loss functions.
result Optimal sketching bounds with rows for sparse norm regression and rows for hinge-like loss functions.
We consider an enlarged dimension reduction space in functional inverse regression. Our operator and functional analysis based approach facilitates a compact and rigorous formulation of the functional inverse regression problem. It also enables us to expand the possible space where the dimension reduction functions bel…
Gradient EM converges exponentially to optimal solution in agnostic mixtures.
problem Fitting parametric functions to given data points without a generative model.
method Gradient EM algorithm for agnostic mixtures of arbitrary parametric functions.
result Gradient EM converges exponentially to population loss minimizers with high probability.
The paper provides risk bounds for learning many response functions using linear regression.
problem Learning many response functions from a single dataset.
method Ordinary least squares regression in a high-dimensional feature space.
result Convergence guarantees on worst-case excess prediction risk for infinite response functions with finite VC dimension.
Multiple Adaptive Bayesian Linear Regression for Scalable Bayesian Optimization with Warm Startstat.ML
Bayesian optimization (BO) is a model-based approach for gradient-free black-box function optimization. Typically, BO is powered by a Gaussian process (GP), whose algorithmic complexity is cubic in the number of evaluations. Hence, GP-based BO cannot leverage large amounts of past or related function evaluations, for e…
The problem of subgroups is ubiquitous in scientific research (ex. disease heterogeneity, spatial distributions in ecology...), and piecewise regression is one way to deal with this phenomenon. Morse-Smale regression offers a way to partition the regression function based on level sets of a defined function and that fu…
Many applications that use empirically estimated functions face a curse of dimensionality, because the integrals over most function classes must be approximated by sampling. This paper introduces a novel regression-algorithm that learns linear factored functions (LFF). This class of functions has structural properties …
New AMP algorithm estimates signals and latent variables in mixed regression models.
problem Estimating signals and latent variables in mixed regression models.
method Approximate Message Passing (AMP) algorithm for matrix GLM.
result State evolution recursion and optimal denoising functions for precise error minimization.
The paper tackles domain generalization using functional regression.
problem Learning a model that generalizes well across different source distributions.
method Functional regression approach to learn a linear operator between marginal and conditional distributions.
result The proposed algorithm achieves finite sample error bounds for the idealized risk.
In this paper, we present a new statistical approach to the problem of incorporating experimental observations into a mathematical model described by linear partial differential equations (PDEs) to improve the prediction of the state of a physical system. We augment the linear PDE with a functional that accounts for th…
The article describe the model, derivation, and implementation of variational Bayesian inference for linear and logistic regression, both with and without automatic relevance determination. It has the dual function of acting as a tutorial for the derivation of variational Bayesian inference for simple models, as well a…
This article considers algorithmic and statistical aspects of linear regression when the correspondence between the covariates and the responses is unknown. First, a fully polynomial-time approximation scheme is given for the natural least squares optimization problem in any constant dimension. Next, in an average-case…
Nonlinear kernel regression models are often used in statistics and machine learning because they are more accurate than linear models. Variable selection for kernel regression models is a challenge partly because, unlike the linear regression setting, there is no clear concept of an effect size for regression coeffici…
Study improves hypothesis transfer learning for functional linear models.
problem Incompatible TL techniques for high-dimensional FLR methods due to infinite-dimensional nature of functional data.
method Proposes two algorithms for hypothesis transfer learning in RKHS framework, leveraging RKHS distance and aggregation techniques.
result Establishes asymptotic lower bounds and matching upper bounds for the proposed algorithms, demonstrating their effectiveness.
Bayesian Additive Distribution Regression (DistBART) predicts distributions from grouped data.
problem Predicting distributions from grouped data with varying characteristics.
method Bayesian nonparametric approach using BART for modeling the regression function.
result Empirical and theoretical evidence supports DistBART's effectiveness in learning from low-dimensional marginals.
BART and MOTR-BART improve tree-based predictions with local linear models.
problem Non-linearity and high-order interactions in data.
method Bayesian Additive Regression Trees (BART) and Model Trees BART (MOTR-BART) using piecewise linear functions.
result MOTR-BART achieves equal or better performance with fewer trees than BART.
Proposes a non-crossing deep neural network quantile regression method.
problem Quantile crossing in nonparametric quantile regression.
method Non-crossing constraints via rectified linear unit penalty function.
result Established non-asymptotic upper bounds for excess risk.
Paper analyzes EM algorithm's trajectory in 2MLR, revealing cycloid behavior.
problem Understanding the convergence and trajectory of EM algorithm in 2MLR.
method Explicit closed-form expressions for EM updates, recurrence relation derivation at population level.
result EM iterations lie on a cycloid trajectory, leading to theoretical estimate of convergence exponent.
Machine learning improves joint default assessment by capturing non-linear dependencies.
problem Capturing non-linear dependencies among covariates for accurate joint default assessment.
method Application of machine learning techniques to credit card dataset, comparing with logistic regression.
result Machine learning outperforms logistic regression in assessing portfolio riskiness.
We develop a multi-kernel based regression method for graph signal processing where the target signal is assumed to be smooth over a graph. In multi-kernel regression, an effective kernel function is expressed as a linear combination of many basis kernel functions. We estimate the linear weights to learn the effective …
We consider the finite sample properties of the regularized high-dimensional Cox regression via lasso. Existing literature focuses on linear models or generalized linear models with Lipschitz loss functions, where the empirical risk functions are the summations of independent and identically distributed (iid) losses. T…
VOL optimizes RL with sparse rewards using weighted bounds.
problem Sparse rewards and non-linear function approximation in RL.
method VOL combines -learning with weighted bounds for optimal regret.
result Achieves asymptotically optimal regret for linear function approximation.
Efficiently recovers piecewise linear functions from noisy samples.
problem Recovering a piecewise linear function from noisy samples with unknown segmentation.
method Iterative merging approach for multidimensional segmented regression.
result First sample and computationally efficient algorithm in any fixed dimension.
Modified ReLU networks improve regression estimation rates.
problem Regression estimation with smooth functions.
method Using modified ReLU neural networks with specific weight modifications.
result Empirical risk minimizers achieve minimax rate of prediction.
A successful approach to structured learning is to write the learning objective as a joint function of linear parameters and inference messages, and iterate between updates to each. This paper observes that if the inference problem is "smoothed" through the addition of entropy terms, for fixed messages, the learning ob…
Optimal AFs minimize RFR test error and sensitivity.
problem Finding optimal AFs for RFR to minimize test error and sensitivity.
method Closed-form solution for AFs minimizing test error and sensitivity under different functional parsimony.
result Optimal AFs can be linear, saturated linear, or Hermite polynomial expressions.
In this paper, we introduce a large class of convergent numerical methods, based on (linear) basis function regression technique, to approximate the solution to a forward-backward stochastic differential equation with jumps (FBSDEJ hereafter). Numerical experiment shows good applicability of the proposed method.
Paper tackles functional linear regression using spectral algorithms with discrete observations.
problem Functional linear regression problem with discretely observed data.
method Combines distributed spectral algorithms with Sobolev kernels for regularization.
result Derives matching upper and lower bounds for convergence in Sobolev norm.
SPQR package uses neural networks for flexible quantile regression.
problem Flexible modeling of non-linear relationships in quantile regression.
method Monotonic splines and neural networks for density estimation; model-agnostic covariate effects.
result Allows for non-linear and quantile-specific effects.
The paper examines efficient algorithms for linear regression over resource-limited networks.
problem Efficient communication in distributed learning over resource-limited networks.
method Developed algorithms for communication-efficient learning of linear regression tasks.
result The algorithms enable a tradeoff between communication and learning with theoretical performance guarantees.
Quantile regression with ReLU networks achieves minimax rates for various function types.
problem Estimating quantiles from covariates with neural networks.
method Quantile regression with rectified linear unit (ReLU) neural networks.
result ReLU networks achieve minimax rates for broad collections of function types.
The paper deals with regression problems, in which the nonsmooth target is assumed to switch between different operating modes. Specifically, piecewise smooth (PWS) regression considers target functions switching deterministically via a partition of the input space, while switching regression considers arbitrary switch…