Algorithm optimizes quantized isotonic regression with log-linear time updates.
problem Optimizing quantized isotonic regression estimations.
method Modified PAVA algorithm for sequential optimization.
result Log-linear time updates for optimal quantized mapping.
Sequential coordinate ascent is more robust in high-dimensional linear regression.
problem Behavior difference between sequential and parallel coordinate ascent in variational inference.
method Comparison of sequential and parallel coordinate ascent algorithms in high-dimensional linear regression.
result Sequential algorithm converges under more relaxed conditions than parallel algorithm.
New bounds for sequential linear regression with square loss, uniformly over all features.
problem Uniform regret bounds for online linear regression with square loss over arbitrary deterministic sequences.
method Derives new regret bounds for online linear regression with square loss, using variants of online non-linear ridge regression.
result Optimal constant of 1 in front of the dB2lnT term for known features, and asymptotic regret bound of dB2lnT for sequentially revealed features. The paper improves SVR with linear constraints for better model properties.
problem Improving Support Vector Regression with linear constraints.
method Generalized SMO algorithm for solving optimization with linear constraints.
result The proposed method shows better practical performance on various datasets.
Mix-IRLS solves imbalanced mixed linear regression problems efficiently.
problem Imbalanced mixed linear regression problems.
method Sequential robust regression approach.
result Mix-IRLS outperforms other methods on imbalanced mixtures and real-world datasets.
A new algorithm splits Gaussian processes for efficient streaming data.
problem Poor scaling of Gaussian processes in streaming data.
method Sequential partitioning of input space and localized Gaussian process fitting.
result The algorithm achieves linear memory complexity and superior time and space complexity.
Develops fast approximations for conditional Shapley values in linear and polynomial models.
problem Estimating conditional Shapley values using regression models is computationally expensive.
method A new approximative estimation method for conditional Shapley values using linear and polynomial regression models.
result Our method significantly reduces computation time compared to existing methods.
We establish optimal rates for online regression for arbitrary classes of regression functions in terms of the sequential entropy introduced in (Rakhlin, Sridharan, Tewari, 2010). The optimal rates are shown to exhibit a phase transition analogous to the i.i.d./statistical learning case, studied in (Rakhlin, Sridharan,…
OOMP selects features online for sparse linear regression.
problem Feature selection in high-dimensional sparse linear models.
method Online algorithm that alternates between feature selection and coefficient estimation.
result Theoretical guarantees and computational complexity analysis of OOMP.
New adaptive models improve prediction accuracy with missing data.
problem Improving prediction accuracy with missing data entries.
method Adaptive optimization approach, learning imputation and regression simultaneously.
result 2-10% improvement in out-of-sample accuracy in strongly non-random missing data settings.
New insights into continual learning for deep models, showing convergence issues but local linear solutions.
problem Challenges in continual learning for homogeneous deep models.
method Sequential projections onto task margin sets, leveraging nonconvex projection theory.
result Local linear convergence under certain conditions for homogeneous deep networks.
Unified framework SVAM learns GLMs robustly to adversarial label corruption.
problem Learning GLMs under adversarial label corruption.
method SVAM framework based on variance reduction technique.
result Provable model recovery guarantees superior to state-of-the-art.
We study nonlinear regression of real valued data in an individual sequence manner, where we provide results that are guaranteed to hold without any statistical assumptions. We address the convergence and undertraining issues of conventional nonlinear regression methods and introduce an algorithm that elegantly mitigat…
Improved bounds for unbounded losses using transductive priors.
problem Sequential regression and classification with unbounded losses.
method Exponential weights algorithm with transductive priors.
result Statistical bounds independent of design vectors and optimal solution norm.
The paper develops a state-space approach to deep Gaussian processes for efficient state estimation.
problem Efficient regression and state estimation for deep Gaussian processes.
method Hierarchical transformed Gaussian process priors, state-space representation, linear stochastic differential equations, sequential methods.
result The state-space approach enables efficient state estimation and regression for deep Gaussian processes.
A universal framework for constructing confidence sets using sequential likelihood mixing.
problem Constructing reliable confidence sets for realizable likelihood functions.
method Sequential likelihood mixing, integrating Bayesian inference and regret inequalities.
result Establishes fundamental connections and provable coverage guarantees for various inference techniques.
Paper tackles uncertainty prediction for deep sequential regression.
problem Challenges in generating accurate uncertainty estimates for deep recurrent networks.
method Flexible method that generates symmetric and asymmetric uncertainty estimates without stationarity assumptions.
result Outperforms competitive baselines on both drift and non-drift scenarios.
Paper proposes an online sparse linear regression method for streaming data.
problem Sparse regression for variable selection and prediction accuracy.
method Online sparse linear regression framework with memory efficiency and relaxed assumptions.
result The ℓ2-norm statistical error of the estimator diminishes to zero with optimal order. Auto-regressive models learn latent states from partially observed linear dynamical systems.
problem Understanding how auto-regressive models learn latent representations from partially observed linear dynamical systems.
method Empirical risk minimization on partially observed linear dynamical systems.
result Two-layer linear auto-regressive models learn to approximate Kalman filtering, coinciding with optimal state estimates.
Sparse linear regression, which entails finding a sparse solution to an underdetermined system of linear equations, can formally be expressed as an l0-constrained least-squares problem. The Orthogonal Least-Squares (OLS) algorithm sequentially selects the features (i.e., columns of the coefficient matrix) to greedil…
This paper establishes minimax rates for online regression with arbitrary classes of functions and general losses. We show that below a certain threshold for the complexity of the function class, the minimax rates depend on both the curvature of the loss function and the sequential complexities of the class. Above this…
Sequential regression procedures can include spurious variables early, even in sparse settings.
problem Sequential regression procedures can select spurious variables early in rankings.
method Analysis of three sequential procedures: forward stepwise, lasso, and least angle regression.
result The first spurious variable is selected earlier as coefficients become denser.
A new algorithm for non-stationary linear bandits with improved regret bound.
problem Non-stationary linear bandit problem with time-varying rewards.
method D-LinUCB, a discounted linear regression algorithm with exponential weights.
result Upper bound on dynamic regret of order d^{2/3} B_T^{1/3}T^{2/3}, optimal in slowly-varying and abruptly-changing environments.
This study examines how sequential correlations affect in-context learning in sequence models.
problem Understanding how in-context learning works with sequentially correlated data.
method Extended linear regression model to sequentially correlated data, tested on transformer architectures.
result Sequential correlations alter the effective context length and attention architecture effectiveness.
Prediction in a small-sized sample with a large number of covariates, the "small n, large p" problem, is challenging. This setting is encountered in multiple applications, such as precision medicine, where obtaining additional samples can be extremely costly or even impossible, and extensive research effort has recentl…
This paper applies deep learning to ordinal regression, modeling it as a binary search.
problem Ordinal regression with deep learning models.
method Formulated ordinal regression as a binary search problem, using recurrent neural networks.
result Deep learning model shows comparable or better predictive power compared to traditional methods.
Paper proposes a debiased estimator for adaptive linear regression.
problem Non-normal asymptotic behavior of OLS estimator in adaptive linear regression.
method Adaptive linear estimating equations to construct debiased estimator.
result Established asymptotic normality of the debiased estimator.
PopArt efficiently solves sparse linear bandits with tighter recovery guarantees.
problem Sparse linear bandits where rewards depend on a few covariates.
method PopArt: a simple, computationally efficient sparse linear estimation method.
result Improved regret bounds compared to state-of-the-art algorithms.
This paper improves prediction in small data sets by eliciting expert knowledge about feature similarities.
problem Improving predictive models from small high-dimensional data sets.
method Eliciting expert knowledge about pairwise feature similarities and using sequential decision making techniques.
result Improvement in predictive performance on both simulated and real data.
New method speeds up change-point detection in data sequences.
problem Efficiently detecting change-points in long data sequences.
method Sequential Gradient Descent and Quasi-Newton's Method.
result New method can be orders of magnitude faster than existing methods.
Overparameterization helps prevent forgetting in sequential learning tasks.
problem Catastrophic forgetting in continual learning systems.
method Analytical study of gradient descent with linear regression model.
result Overparameterization can mitigate forgetting in a two-task setting.
This paper studies statistical estimation in optional regression models.
problem Estimating parameters in regression models with optional semimartingale processes.
method Structural least squares (LS) estimates and their sequential versions.
result Strong consistency of LS-estimates and fixed accuracy of sequential LS-estimates.
Stochastic gradient descent (SGD) is a well known method for regression and classification tasks. However, it is an inherently sequential algorithm at each step, the processing of the current example depends on the parameters learned from the previous examples. Prior approaches to parallelizing linear learners using SG…
Sparse Gaussian process quantile regression tackles computational challenges in Bayesian quantile regression.
problem Nonconjugacy and computational cost in Gaussian process quantile regression.
method Sparse Gaussian process framework with Laplace approximation, adaptive inducing-input placement, and sequential data acquisition.
result Accuracy of Laplace approximation and effectiveness of adaptive mechanisms in reducing predictive uncertainty.
New tighter confidence bounds for sequential kernel regression.
problem Quantifying uncertainty in sequential learning algorithms.
method Martingale tail inequalities and conic programming.
result New confidence bounds are tighter than existing ones.
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.
Develops new techniques for learning from sequential data groups.
problem Learning from groups of inputs rather than individual inputs.
method Introduces feature-based and kernel-based learning techniques for sequential data.
result Achieves state-of-the-art performance on various real-world examples.
A key limitation of sampling algorithms for approximate inference is that it is difficult to quantify their approximation error. Widely used sampling schemes, such as sequential importance sampling with resampling and Metropolis-Hastings, produce output samples drawn from a distribution that may be far from the target …
We consider the problem of online linear regression on individual sequences. The goal in this paper is for the forecaster to output sequential predictions which are, after T time rounds, almost as good as the ones output by the best linear predictor in a given ℓ1-ball in Rd. We consider both the cases wher…
Active learning method reduces labeling cost for regression models with aggregated data.
problem Reducing labeling cost for training regression models with aggregated data.
method Sequentially selects sets to be labeled using mutual information quantifying model parameter uncertainty.
result Achieves better predictive performance with fewer labeled sets.
The paper connects a proximal method to stochastic filters and Bayes updates.
problem Large-scale optimization and probabilistic methods for regression.
method Explicit form of Bayes updates for linear regression and general sequential setting.
result The incremental proximal method can be realized by the Kalman filter for linear-quadratic cost functions.
This paper improves pool-based sequential active learning for regression.
problem Efficiently selecting unlabeled samples for regression models.
method Proposes three criteria (informativeness, representativeness, diversity) and a new ALR approach using passive sampling.
result The new ALR approach significantly improves model performance across various domains.
A new method for efficient ordinal regression.
problem Efficiently modeling ordinal relationships in multi-label learning.
method Incremental Sparse Bayesian Ordinal Regression (ISBOR) approach.
result ISBOR achieves accurate predictions with fewer basis functions.
Proposes a new adaptive design strategy for discontinuous regression functions.
problem Designing input variables for discontinuous regression functions.
method Sequential adaptive design strategy using statistical properties.
result Effective design points selection for discontinuous regression functions.
Efficient algorithm for near-optimal online learning with generalized linear functions.
problem Exponential gap between statistically optimal regret and efficient regret for some function classes.
method Computational efficient algorithm for realizable K-wise linear classification and over-parameterized polynomial featurization.
result First algorithm with log(T/σ) regret for realizable K-wise linear classification.
Many model selection algorithms produce a path of fits specifying a sequence of increasingly complex models. Given such a sequence and the data used to produce them, we consider the problem of choosing the least complex model that is not falsified by the data. Extending the selected-model tests of Fithian et al. (2014)…
The overarching goal of this paper is to derive excess risk bounds for learning from exp-concave loss functions in passive and sequential learning settings. Exp-concave loss functions encompass several fundamental problems in machine learning such as squared loss in linear regression, logistic loss in classification, a…
An AI approach selects variables in linear models.
problem Selecting significant variables in linear regression models.
method Artificial Neural Network trained to determine variable significance based on OLS estimates.
result The AI approach outperforms traditional methods in accuracy and variable selection.