The paper develops predictors for functional data on manifolds.
problem Functional data prediction on time-varying manifolds.
method Least-squares local linear Fréchet curve predictor and weighted Fréchet mean approach.
result Asymptotical optimality of the proposed predictors.
We analyze the (unconditional) distribution of a linear predictor that is constructed after a data-driven model selection step in a linear regression model. First, we derive the exact finite-sample cumulative distribution function (cdf) of the linear predictor, and a simple approximation to this (complicated) cdf. We t…
We study online linear regression problems in a distributed setting, where the data is spread over a network. In each round, each network node proposes a linear predictor, with the objective of fitting the \emph{network-wide} data. It then updates its predictor for the next round according to the received local feedbac…
New method converts LVAs into linear projections for better understanding of complex models.
problem Limited interpretability of nonlinear machine learning models.
method Animated linear projections and radial tours.
result Improved understanding of variable importance in complex models.
Recent results in the literature indicate that a residual network (ResNet) composed of a single residual block outperforms linear predictors, in the sense that all local minima in its optimization landscape are at least as good as the best linear predictor. However, these results are limited to a single residual block …
In this work, we study the problem of aggregating a finite number of predictors for nonstationary sub-linear processes. We provide oracle inequalities relying essentially on three ingredients: (1) a uniform bound of the ℓ1 norm of the time varying sub-linear coefficients, (2) a Lipschitz assumption on the predict…
New method selects sparse predictors in large LMMs.
problem Sparse learning for LMMs is computationally infeasible for large datasets.
method Developed an ℓ0 regularized method with coordinate descent and local search algorithms. result Method selects thousands of predictors in seconds to minutes.
New bounds show linear predictors rarely overfit with certain optimization methods.
problem Bounding test error for linear predictors with stochastic optimization methods.
method Coupling argument for fixed point methods like stochastic and batch mirror descent.
result Locally-adapted rates that depend on predictor properties, not global problem structure.
A predictor that is deployed in a live production system may perturb the features it uses to make predictions. Such a feedback loop can occur, for example, when a model that predicts a certain type of behavior ends up causing the behavior it predicts, thus creating a self-fulfilling prophecy. In this paper we analyze p…
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.
A residual network (or ResNet) is a standard deep neural net architecture, with state-of-the-art performance across numerous applications. The main premise of ResNets is that they allow the training of each layer to focus on fitting just the residual of the previous layer's output and the target output. Thus, we should…
New sample complexity bounds for linear predictors and neural networks, focusing on initialization.
problem Understanding sample complexity for vector-valued linear predictors and neural networks, especially under initialization-dependent conditions.
method Size-independent bounds on Frobenius norm distance from a fixed reference matrix, applying to vector-valued predictors and neural networks.
result Established new sample complexity bounds for feed-forward neural networks, resolving open questions and introducing a new learnable problem.
This paper proposes a method to reduce complexity in GLMs with categorical predictors.
problem Wasteful, hard-to-interpret, and prone to overfitting of traditional one-hot encoding for high-cardinality categorical predictors.
method Clustering categories of categorical predictors through a numerical method that preserves or improves accuracy while reducing the number of coefficients.
result Clustering categories of categorical predictors reduces complexity substantially without harming accuracy.
LESS combines local predictors for subsets to learn from heterogeneous input-output pairs.
problem Learning from heterogeneous input-output pairs in populations with varied behavior.
method LESS algorithm: generates subsets, trains local predictors, combines them.
result LESS is highly competitive compared to state-of-the-art methods.
We provide a new approach to training neural models to exhibit transparency in a well-defined, functional manner. Our approach naturally operates over structured data and tailors the predictor, functionally, towards a chosen family of (local) witnesses. The estimation problem is setup as a co-operative game between an …
Method constructs confidence regions for linear models with arbitrary predictors.
problem Constructing confidence regions for linear models with non-linear predictors.
method Mixed Integer Linear Programming for constraints.
result Empty confidence regions for hypothesis testing.
LIT-LVM improves linear predictors by estimating interaction terms with latent vectors.
problem Accurately estimating coefficients for interaction terms in linear predictors.
method Structured regularization using latent vectors to represent features.
result LIT-LVM achieves superior prediction accuracy compared to other methods.
Linear properties are either universal or absent across language models.
problem Explaining the prevalence of linear properties in language models.
method Proved identifiability of distribution-equivalent next-token predictors and analyzed various notions of linearity.
result Linear properties either hold in all or none distribution-equivalent next-token predictors.
Study shows linear predictors fail with missing data, but simpler approximations and neural networks can work.
problem Building predictors with missing data when the target is a linear function of observed data.
method Analyzed the Gaussian case and proposed a linear function of multiway interactions. Studied a simple approximation and proved generalization bounds. Showed multilayer perceptrons with ReLU activation can be consistent.
result Simple approximations and neural networks can be effective in handling missing data, especially with sufficient data.
Optimizing proper loss yields calibrated models under specific conditions.
problem Understanding when optimizing proper loss functions leads to calibrated predictions.
method Local optimality condition and Lipschitz functions.
result Predictors with local optimality are nearly calibrated and nearly locally optimal.
Paper addresses linear regression with partially mismatched data using local search with theoretical guarantees.
problem Linear regression with partially mismatched data.
method Optimization formulation and greedy local search algorithm with theoretical guarantees.
result Local search algorithm converges to nearly-optimal solution at a linear rate under certain conditions.
Overparameterized MLR fits hyper-curves, improving model robustness.
problem Improper predictors degrade model generalizability.
method Parameterizing with a scalar and monomial basis, fitting hyper-curves.
result Hyper-curve approach yields robust predictions for noisy data.
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.
Predict covariance from features using convex optimization.
problem Predicting the covariance of a Gaussian vector from another feature vector.
method A generalized linear model with convex optimization for fitting parameters.
result Predicted covariance matrices are symmetric positive definite.
Study on merging predictors in causal and anticausal directions using CMAXENT.
problem Comparing merging predictors in causal and anticausal directions.
method Using CMAXENT as inductive bias, study differences in merging predictors.
result CMAXENT solution reduces to logistic regression in causal direction and LDA in anticausal direction.
In machine learning and data mining, linear models have been widely used to model the response as parametric linear functions of the predictors. To relax such stringent assumptions made by parametric linear models, additive models consider the response to be a summation of unknown transformations applied on the predict…
Novel strategy for federated learning with privacy-preserving predictors and nonvacuous generalization bounds.
problem Privacy-preserving federated learning with nonvacuous generalization bounds.
method Randomized predictors, PAC-Bayesian generalization bound, synchronous and heterogeneous/homogenous cases.
result Achieves comparable predictive performance to batch approach while preserving privacy.
Least squares estimator fails to achieve optimal risk in bounded distributions, but non-linear predictors can.
problem Optimal risk in bounded distributions for constrained least squares.
method Comparison of least squares and non-linear predictors.
result Non-linear predictors can achieve optimal risk O(d/n) in bounded distributions. The study finds a trade-off between model size, test loss, and training loss for linear predictors.
problem Finding the optimal balance between model size, test loss, and training loss for linear predictors.
method Established an algorithm and distribution-independent trade-off using non-asymptotic analysis.
result Models with low test loss are either classical (close to noise level training loss) or modern (large number of parameters).
Random imputation is surprisingly effective for linear predictors in missing data scenarios.
problem The effectiveness of naive imputation in missing data scenarios for linear predictors.
method A unique random features model framework to study predictive performances.
result Naive imputation is negligible in bias for linear predictors under MCAR assumption.
We present a method to stop the evaluation of a prediction process when the result of the full evaluation is obvious. This trait is highly desirable in prediction tasks where a predictor evaluates all its features for every example in large datasets. We observe that some examples are easier to classify than others, a p…
A new Bayesian approach to linear system identification has been proposed in a series of recent papers. The main idea is to frame linear system identification as predictor estimation in an infinite dimensional space, with the aid of regularization/Bayesian techniques. This approach guarantees the identification of stab…
Improved classification model for high-cardinality categorical predictors.
problem Handling high-cardinality categorical predictors and non-linear data.
method Data-driven binning of spline functions and shrinkage estimators.
result Improved classification precision with interpretable predictors.
Study tail risk in high-frequency finance using L1-regularized regression.
problem Measuring tail risk dynamics in high-frequency financial markets.
method Dynamic extreme value regression model with L1-regularized maximum likelihood estimator. result Severity of extreme losses well predicted by low price impact in high volatility periods.
This study compares various superlearner and deep learning architectures (machine-learning-based and neural-network-based) for classification problems across several simulated and industrial datasets to assess performance and computational efficiency, as both methods have nice theoretical convergence properties. Superl…
The problem of forecasting conditional probabilities of the next event given the past is considered in a general probabilistic setting. Given an arbitrary (large, uncountable) set C of predictors, we would like to construct a single predictor that performs asymptotically as well as the best predictor in C, on any data.…
In this short note, we provide a sample complexity lower bound for learning linear predictors with respect to the squared loss. Our focus is on an agnostic setting, where no assumptions are made on the data distribution. This contrasts with standard results in the literature, which either make distributional assumption…
Study examines how body segments respond to random vibrations.
problem Understanding human body responses to random vibrations.
method 35 participants were tested with random noise signals. Multiple linear regression models were created to determine influential predictors of peak translational gains.
result Multiple predictors, including motion direction and body segment, significantly influence peak translational gains.
New insights into when benign overfitting occurs in linear and classification tasks.
problem Understanding when benign overfitting happens in linear and classification models.
method Analysis of a generic data model and comparison of predictors (minimum-norm interpolating and max-margin).
result The minimum-norm interpolating predictor is biased towards an inconsistent solution, preventing benign overfitting in linear regression.
Neural Local Wasserstein Regression models distribution-on-distribution regression with flexible, localized transport maps.
problem Estimating distribution-on-distribution regression with global optimal transport maps or linearization limitations.
method Proposes Neural Local Wasserstein Regression, a flexible nonparametric framework using locally defined transport maps in Wasserstein space.
result Demonstrates effective capture of nonlinear and high-dimensional distributional relationships.
Study fairness in ordinal regression using threshold models.
problem Fairness in ordinal regression predictions.
method Adapted fairness notions from fair ranking; use threshold model with scoring function and thresholds; apply binary classification for scoring function and local search for thresholds.
result Generalization guarantees on predictor error and fairness violation; effectiveness demonstrated in experiments.
Generalized Linear Models (GLMs) and Single Index Models (SIMs) provide powerful generalizations of linear regression, where the target variable is assumed to be a (possibly unknown) 1-dimensional function of a linear predictor. In general, these problems entail non-convex estimation procedures, and, in practice, itera…
New probabilistic complexity measures for linear and kernel methods.
problem Limitations of linear and kernel methods in machine learning.
method Introducing approximate notions of dimensional and margin complexity.
result Approximate complexity measures are both sufficient and necessary for learning.
Ensemble methods that average over a collection of independent predictors that are each limited to a subsampling of both the examples and features of the training data command a significant presence in machine learning, such as the ever-popular random forest, yet the nature of the subsampling effect, particularly of th…
Deep neural networks improve AFT model for non-linear predictors.
problem Nonlinearity in predictors of AFT models.
method Apply DNNs to fit AFT models using Gehan-type loss and sub-sampling.
result DeepR-AFT outperforms parametric and semiparametric models.
We analyze the local Rademacher complexity of empirical risk minimization (ERM)-based multi-label learning algorithms, and in doing so propose a new algorithm for multi-label learning. Rather than using the trace norm to regularize the multi-label predictor, we instead minimize the tail sum of the singular values of th…
This paper provides estimation and inference methods for the best linear predictor (approximation) of a structural function, such as conditional average structural and treatment effects, and structural derivatives, based on modern machine learning (ML) tools. We represent this structural function as a conditional expec…
Functional PLS improves prediction and inference for scalar responses from functional predictors.
problem Estimating scalar responses from functional predictors in an ill-posed inverse problem.
method Functional partial least squares (PLS) estimator with adaptive early stopping and new tests.
result PLS attains nearly minimax-optimal convergence rates and detects local alternatives.