We establish linear regret bounds for convex smooth losses using Fenchel-Young losses.
problem Establishing linear regret bounds for convex smooth losses.
method Constructing a convex smooth surrogate loss using Fenchel-Young losses generated by the convolutional negentropy.
result We derive a smooth loss with a linear surrogate regret bound.
New method recovers signals from saturated data using linear loss and nonconvex penalties.
problem Signal recovery from saturated measurements with sign information loss.
method Linear loss and nonconvex penalties (e.g., minimax concave penalty, sorted ℓ1 norm).
result Estimation error is bounded and recovery performance improved.
New protocols for locally private learning of linear models with reduced data leakage.
problem Locally private learning of linear models with minimal data leakage.
method Noninteractive LDP convex optimization protocols for generalized linear losses and Euclidean median problems.
result First algorithms with sub-exponential dependence on dimensionality for nonsmooth losses.
Proposes a new loss function for robust learning.
problem Creating a robust loss function for machine learning.
method Extended pseudo Huber loss with log-exp transform and logistic function.
result Linear convergence algorithm for minimizer finding.
Fast classification for sparse models, even with correlated features.
problem Sparse classification with many correlated features.
method Linear and quadratic surrogate cuts, priority queue, and analytical solution for exponential loss.
result 2 to 5 times faster than previous approaches, interpretable models with comparable accuracy.
Paper introduces structured sparsity estimators for Generalized Linear Models.
problem Estimating structured sparsity in GLMs with debiased estimators.
method Extends Stucky and van de Geer's results to GLMs with structured sparsity.
result Proves oracle inequalities for structured sparsity estimators in GLMs.
Deep linear networks avoid spurious local minima under certain conditions.
problem Existence of spurious local minima in deep linear networks.
method Reduction to two-layer case, quadratic loss analysis, and perturbation argument to show full rank property.
result Deep linear networks have no spurious local minima under specific conditions.
Positive results for agnostic regression with various losses.
problem Agnostic regression with bounded sample compression.
method Generic and efficient sample compression schemes for real-valued functions.
result Exact and approximate compression schemes for specific losses.
Gradient EM converges exponentially to optimal solution in agnostic mixtures.
problem Fitting k 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.
MRCs minimize worst-case expected 0-1 loss and provide performance guarantees.
problem Minimizing expected 0-1 loss in classification.
method Minimizes worst-case expected 0-1 loss over uncertainty sets defined by linear constraints.
result Achieves efficient learning and generalization with performance guarantees.
Study on calibration and consistency of adversarial surrogate losses.
problem Designing robust classifiers with theoretical guarantees.
method Extensive analysis of H-calibration and H-consistency of adversarial surrogate losses.
result Some convex loss functions and supremum-based convex losses are not H-calibrated for important hypothesis sets.
Linear-Core Surrogates combine fast optimization and statistical efficiency in classification and structured prediction.
problem The trade-off between smoothness and margin-based losses in classification and structured prediction.
method Linear-Core (LC) Surrogates, a family of convex loss functions that stitch a linear core to a smooth tail.
result LC Surrogates achieve fast linear consistency rates while maintaining differentiability and strict H-consistency bounds. Study on loss landscapes of deep linear networks using algebraic geometry.
problem Understanding the loss landscapes of deep linear networks.
method Algebraic geometry methods to analyze the properties of the optimization landscapes.
result Deep linear networks have local minima that are not global minima.
ICE algorithm solves exact 0-1 loss linear classification problem efficiently.
problem Exact solution to the 0-1 loss linear classification problem for non-linearly separable data.
method Incremental cell enumeration (ICE) algorithm, leveraging combinatorial and incidence relations.
result First provably optimal algorithm for exact 0-1 loss linear classification problem.
We prove a new generalization bound that shows for any class of linear predictors in Gaussian space, the Rademacher complexity of the class and the training error under any continuous loss ℓ can control the test error under all Moreau envelopes of the loss ℓ. We use our finite-sample bound to directly recover…
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.
This paper consider penalized empirical loss minimization of convex loss functions with unknown non-linear target functions. Using the elastic net penalty we establish a finite sample oracle inequality which bounds the loss of our estimator from above with high probability. If the unknown target is linear this inequali…
New bounds show polyhedral surrogates are optimal for generalization.
problem Proving generalization rates for polyhedral loss functions.
method Developed two general results for polyhedral surrogates.
result Polyhedral surrogates provide linear surrogate regret bounds, translating directly to target rates.
The paper tackles online learning with two types of losses and shows it's impossible without certain assumptions.
problem Online learning with primary and secondary losses where the secondary loss is bounded by a linear threshold.
method Analyzes the feasibility of achieving low regret with respect to the primary loss while keeping the secondary loss within a linear threshold.
result Achieving the goal is impossible without bounded variance assumption on the secondary loss.
Enhances linear regression with Kalman filter for loss minimization.
problem Minimizing loss in linear regression models.
method Integrates Kalman filter and SGD for optimal weight updates.
result Develops optimal linear regression equation with minimum area under curve.
Efficient algorithms find optimal monotone transforms for calibration under strictly convex losses.
problem Calibrating estimations to improve performance with monotone transforms.
method Proposed linear-time and space algorithm for finding optimal monotone transforms for specific loss functions. Also proposed an anytime algorithm with linear space and pseudo-linearithmic time complexity.
result Optimal monotone transforms are unique and can be found efficiently for various strictly convex loss functions.
New scalable algorithm for non-negative linear regression with entropy-regularized OT loss.
problem Generalizing task-specific linear models to broader applications.
method Sinkhorn-like scaling iterations for convex penalty and datafit terms.
result Simple multiplicative updates for various penalty and datafit terms.
The paper justifies time-dependent loss reweighting schemes for flow matching and diffusion models.
problem Theoretical justification for time-dependent loss reweighting schemes in flow matching and diffusion models.
method Clarifies that the loss can depend on both time and state, and shows theoretical justification for time-dependent loss weighting schemes.
result Time-dependent loss weighting schemes are theoretically justified for Generator Matching and Edit Flows.
The study explains delayed spikes in batch-normalized models.
problem Delayed spikes in batch-normalized models.
method Analyzing batch-normalized linear models, deriving conditions for delayed onset and waiting time.
result Explicit conditions for delayed-onset and waiting time in whitened square-loss linear regression.
Proposes a method for inference in high-dimensional classification with non-differentiable surrogate losses.
problem Lack of inference procedures for identifying driving factors in high-dimensional classification with non-differentiable surrogate losses.
method Kernel-smoothed decorrelated score and cross-fitted version for hypothesis tests and interval estimators.
result Valid and superior inference methods for high-dimensional classification with non-differentiable surrogate losses.
Geometric study of linear neural networks identifies pure and spurious critical points.
problem Understanding the landscape of loss functions in linear neural networks.
method Geometric properties of functional spaces and parameterization analysis.
result Different phenomena cause the absence of bad local minima in linear networks, depending on the architecture and loss function.
Adversarial training makes logistic regression weight loss landscapes sharper.
problem Understanding why adversarial training sharpens the weight loss landscape in logistic regression.
method Theoretical analysis of linear logistic regression model with L2 norm constraints, and experiments on ResNet18.
result Adversarial training sharpens the weight loss landscape in linear logistic regression models.
Paper proposes iterative trimmed loss minimization for learning from corrupted data.
problem Learning from corrupted training data.
method Iterative trimmed loss minimization, alternating between selecting and retraining samples.
result Recovery of ground truth with linear convergence rate in generalized linear models.
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).
Develops a gradient-enhanced approach for online estimation in high-dimensional generalized linear models with streaming data.
problem Online estimation for high-dimensional generalized linear models with streaming data.
method Proposes a gradient-enhanced surrogate loss for non-distributed setting and extends to distributed streaming data.
result Derives non-asymptotic error bounds under high-dimensional scaling without batch-number constraint.
Given a task of predicting Y from X, a loss function L, and a set of probability distributions Γ on (X,Y), what is the optimal decision rule minimizing the worst-case expected loss over Γ? In this paper, we address this question by introducing a generalization of the principle of maximum entropy. Applying t…
Given two networks with the same training loss on a dataset, when would they have drastically different test losses and errors? Better understanding of this question of generalization may improve practical applications of deep networks. In this paper we show that with cross-entropy loss it is surprisingly simple to ind…
Paper introduces LPCs for robust classification with performance bounds.
problem Conventional classification techniques constrain rules and use surrogate losses.
method Robust risk minimization (RRM) for unconstrained classification rules, optimizing 0-1 loss.
result LPCs provide performance bounds and competitive performance with state-of-the-art techniques.
Researchers improve visualization of neural network loss landscapes.
problem Understanding neural network generalization performance.
method Novel 'jump and retrain' procedure, non-linear dimensionality reduction (PHATE), computational homology.
result Improved visualization and quantification of neural network generalization performance.
Develops active learning method for linear optimization with margin-based criterion.
problem Optimizing decisions in linear optimization problems with limited labeled data.
method Smart Predict-then-Optimize (SPO) loss and margin-based active learning algorithm.
result Algorithm achieves significantly fewer labels than naive supervised learning, especially for minimizing SPO loss.
Piecewise linear activations create many spurious local minima in neural networks.
problem Understanding the loss surface of neural networks with piecewise linear activations.
method Proved the existence of infinite spurious local minima and partitioned the loss surface into smooth cells.
result Piecewise linear activations create many spurious local minima that are invariant under a continuous path.
Unified framework connects different neural network models.
problem Understanding the geometry of neural network loss landscapes.
method Unified framework capturing four symmetry classes.
result First discovery of low- and zero-barrier linear interpolation paths.
Theory integrates loss aversion into expected utility for monetary returns.
problem Modeling loss aversion in expected utility theory.
method Develops state-dependent linear utility functions incorporating loss aversion.
result Contracts from monopolists in insurance markets.
Study analyzes landscape complexity of empirical loss functions with correlated data.
problem Understanding the complexity of loss landscapes in machine learning with structured data.
method Kac-Rice formula and random matrix theory applied to high-dimensional empirical loss functions.
result Characterizes the average number of critical points in loss functions with structured data.
LQF linearizes deep models for better interpretability.
problem Lack of interpretability in deep neural networks.
method Simple modifications to architecture, loss function, and optimization.
result Comparable performance to non-linear fine-tuning, with interpretability.
Principal component regression (PCR) is a widely used two-stage procedure: principal component analysis (PCA), followed by regression in which the selected principal components are regarded as new explanatory variables in the model. Note that PCA is based only on the explanatory variables, so the principal components a…
In deep learning, \textit{depth}, as well as \textit{nonlinearity}, create non-convex loss surfaces. Then, does depth alone create bad local minima? In this paper, we prove that without nonlinearity, depth alone does not create bad local minima, although it induces non-convex loss surface. Using this insight, we greatl…
Study nonparametric density estimation under Besov IPM losses and GANs.
problem Estimating nonparametric densities under various loss functions.
method Provide lower and upper bounds for convergence rates, formalize GANs as statistical models.
result IPMs can improve GANs' performance over linear estimators.
Improved privacy bounds for learning linear predictors with convex losses.
problem Differentially private learning of linear predictors with convex losses.
method Developed private model selection approach to achieve optimal rates.
result Improved upper and lower bounds for excess population risk.
New algorithms for differentially private optimization in convex and non-convex settings with near-optimal rates.
problem Differentially private optimization in convex and non-convex settings.
method Developed algorithms for convex and non-convex settings with near-optimal excess population risk.
result Achieved near-optimal rates in near-linear time for convex settings and nearly dimension independent rates for non-convex settings.
This work proposes a mathematical framework for loss landscapes and optimization in deep neural networks.
problem The effectiveness of gradient-based optimization in over-parameterized neural networks.
method A modern view and mathematical framework of loss landscapes and efficient optimization in over-parameterized machine learning models.
result Wide neural networks satisfy the PL∗ condition, explaining (S)GD convergence to a global minimum. We carefully study how well minimizing convex surrogate loss functions, corresponds to minimizing the misclassification error rate for the problem of binary classification with linear predictors. In particular, we show that amongst all convex surrogate losses, the hinge loss gives essentially the best possible bound, o…
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.