BlitzWS is a working set algorithm for convex problems with theoretical guarantees.
problem Optimizing subproblem size and stopping criteria for working set algorithms.
method BlitzWS proposes a principled approach with theoretical guarantees, optimizing subproblem size and stopping criteria based on progress.
result BlitzWS achieves fast convergence times for convex problems, including L1-regularized models and support vector machines.
New solver speeds up Lasso-type problems by using screening rules and working sets.
problem Efficiently solving large-scale Lasso-type problems.
method Combining Gauss-Southwell rule with aggressive Gap Safe screening rules and working set strategy.
result Achieves state-of-the-art performance on sparse learning problems.
This work establishes properties on diffeological structures for set-valued maps and measures.
problem Establish rigorous properties on diffeological structures for set-valued maps and measures.
method Using diffeologies, the authors link various structures including set-valued maps, relations, gradients, measures, and shape analysis.
result Established rigorous properties on sample diffeologies.
Paper proposes a working set algorithm for non-convex sparse regression with provable convergence.
problem Estimating sparse linear models from high-dimensional data using non-convex regularizers.
method FireWorks algorithm based on non-convex reformulation and leveraging residual geometry.
result Convergence to a stationary point of the full problem with provable guarantees.
This work examines aggregation functions in Deep Set learning.
problem The sensitivity of Deep Set networks to aggregation function choices.
method Investigation of alternative aggregation functions, including learnable recurrent ones.
result Learnable aggregations improve performance, reduce hyper-parameter sensitivity, and generalize better.
We found a new simple family of Cantor sets whose projections are one-dimensional.
problem Finding simple Cantor sets with specific projection properties.
method Developed a new series of self-similar Cantor sets in R3. result All projections of these new Cantor sets are connected and one-dimensional.
WHInter solves high-dimensional sparse interaction models efficiently.
problem Learning sparse models with two-way interactions in high-dimensional data.
method Working set algorithm for l1-regularised problems with quadratic interactions.
result Two orders of magnitude faster than state-of-the-art methods.
The C-bound, introduced in Lacasse et al., gives a tight upper bound on the risk of a binary majority vote classifier. In this work, we present a first step towards extending this work to more complex outputs, by providing generalizations of the C-bound to the multiclass and multi-label settings.
New condition for reconstructing Morse functions on 3D manifolds.
problem Reconstructing Morse functions with specific level sets.
method Studied a necessary and sufficient condition for reconstruction.
result New condition strengthens previous sufficient conditions.
Algorithm estimates Gaussian parameters under unknown truncation sets.
problem Estimating Gaussian parameters when samples are truncated to unknown sets.
method Efficient algorithm for arbitrary unknown truncation sets, using Gaussian surface area as complexity measure.
result Algorithm works for large families of sets including intersections of halfspaces and general convex sets.
The paper outlines future work in random sets theory.
problem Developing a theory of statistical reasoning with random sets.
method Generalizing logistic regression, probability laws, and geometric uncertainty.
result A new geometric approach to uncertainty with general random sets.
Algorithm tackles constrained reinforcement learning with concave-convex and knapsack constraints.
problem Constrained episodic reinforcement learning with concave rewards and convex constraints.
method Modular analysis with strong theoretical guarantees for concave-convex and knapsack settings.
result Significantly outperforms existing approaches in constrained episodic environments.
Improved RL algorithm with linear MDPs for offline learning with partial data coverage.
problem Efficient offline RL with linear MDPs under partial data coverage.
method Primal-dual algorithm with O(ε−2) sample complexity. result First computationally efficient algorithm with O(ε−2) sample complexity for offline RL with linear MDPs under partial data coverage. Proposes a robust method for high-dimensional linear models.
problem Inference in high-dimensional settings with heavy-tailed errors and clustered data.
method Residual randomization procedure for Lasso-based inference.
result Outperforms state-of-the-art methods in challenging settings.
This work extends set-valued risk measures to discrete time, using difference inclusions and equations.
problem Defining set-valued dynamic risk measures in discrete time.
method Investigates discrete time setting with difference inclusions and difference equations.
result Provides insights for continuous time representations of set-valued dynamic risk measures.
New algorithms prove fast convergence in complex min-max problems.
problem Proving fast convergence in nonconvex min-max optimization.
method Hamiltonian Gradient Descent (HGD) and Consensus Optimization (CO) algorithms.
result HGD and CO achieve linear convergence in various settings.
New estimates show unique cylindrical blow-ups for Dirichlet energy minimizers near singular points.
problem Analyzing the singularities of multi-valued Dirichlet energy minimizers.
method Developed estimates to study asymptotic behavior and used techniques from Wickramasekera's work.
result The singular set of a Dirichlet energy minimizer is countably (n−2)-rectifiable. New framework captures non-autonomous IFS limit set topology.
problem Understanding topological properties of non-autonomous IFS limit sets.
method Homological framework applied to fractal square.
result Provides insights into fractal topology, answering Mandelbrot's percolation problem.
This work extends learning theory to complexly dependent data under Dobrushin's condition.
problem Learning from weakly dependent data sampled on networks or spatial domains.
method Developed complexity measures and learning bounds for hypothesis classes under Dobrushin's condition.
result Generalization and learnability bounds degrade by constant and log factors compared to i.i.d. settings.
The paper tackles Kakeya and Nikodym sets on curved manifolds, reducing problems to Euclidean space.
problem Analyzing Kakeya and Nikodym sets on curved manifolds.
method Reduction of problems on curved manifolds to Euclidean space, using Bourgain's condition and recent breakthroughs.
result Establishes the Nikodym conjecture for three-dimensional manifolds with constant sectional curvature.
Given a simple algebraic group G, a web is a directed trivalent graph with edges labelled by dominant minuscule weights. There is a natural surjection of webs onto the invariant space of tensor products of minuscule representations. Following the work of Westbury, we produce a set of webs for $\SL_n$ which form a bas…
This work introduces COLA, a strategy to aggregate conformal prediction sets efficiently.
problem Efficiently combining multiple conformity scores to reduce prediction set size.
method Introduces COnfidence-Level Allocation (COLA) to optimally allocate confidence levels across sets.
result COLA achieves smaller prediction sets than state-of-the-art methods while maintaining valid coverage.
Study of mean curvature flow with obstacles using singular perturbation.
problem Obstacle problem associated to mean curvature flow.
method Geometric vanishing-viscosity approximation with singular perturbation.
result Generic level sets are distributional solutions of the obstacle problem.
ExNODE uses ODE to model sets with permutation equivariance.
problem Capturing intra-set dependencies in unordered sets.
method Exchangeable Neural ODE (ExNODE) using ODE.
result ExNODE achieves permutation equivariance for set modeling.
New algorithms learn sparse set functions in non-orthogonal Fourier bases.
problem Learning sparse set functions in non-orthogonal Fourier bases.
method Novel algorithms using non-orthogonal Fourier transforms.
result At most nk−klog2k+k queries for k non-zero Fourier coefficients. This work introduces a noise-adaptive conformal inference method for better prediction sets in noisy data.
problem Real-world complications like random label noise limit the effectiveness of conformal inference.
method An adaptive conformal inference method capable of handling deviations from exchangeability.
result Informative prediction sets with tight marginal coverage guarantees in noisy data.
Improved regret bounds for structured linear contextual bandits with Gaussian noise.
problem Optimizing bandit learning algorithms for structured contexts with Gaussian perturbations.
method Proposed simple greedy algorithms for structured linear contextual bandits with Gaussian noise.
result Unified regret analysis for structured parameters with geometric quantities as bounds.
Optimal ANN pre-training with SDA reduces handwritten Bengali digit recognition error to 2.34%
problem Optimizing ANN architecture for Bengali handwritten digit recognition
method Pre-training ANN with stacked denoising autoencoder (SDA)
result Minimum validation error of 2.34% on handwritten Bengali dataset
New method for scalable set encoding with unbiased gradient approximation.
problem Limited expressive power and large set training issues in set functions.
method Universally MBC (UMBC) class of set functions and efficient MBC training algorithm.
result Unbiased approximation of full set gradient with constant memory overhead.
Study fixed points in digital images, introducing new invariants.
problem Understanding properties of digital images through fixed points.
method Introduce new invariants and freezing/cold sets to analyze fixed point sets.
result Existence of fixed point sets restricts maps on their complements.
This work introduces online meta-learning, merging paradigms to enhance continual learning.
problem Continuous learning of new tasks with fast adaptation.
method Follow the meta leader algorithm, extending MAML to online setting with theoretical guarantees.
result Significant performance improvement over traditional online learning approaches.
This work tackles robust Bayesian optimization under data shift using φ-divergences.
problem Bayesian optimization under uncertainty and data shift.
method Distributionally robust optimization with φ-divergences.
result A computationally tractable algorithm with provable sublinear regret bounds.
New gradient coding schemes reduce decoding error in both random and adversarial straggler settings.
problem Creating efficient approximate gradient coding schemes for distributed optimization.
method Introduced novel approximate gradient codes based on expander graphs, achieving optimal decoding coefficients.
result Achieved nearly optimal error in random setting and nearly half the error in adversarial setting compared to existing codes.
New results show contrastive learning can recover shared factors in multimodal data.
problem Understanding when contrastive learning can recover shared latent factors in multimodal data.
method New identifiability results for multimodal contrastive learning, distinguishing between multi-view and multimodal settings.
result Contrastive learning can block-identify shared latent factors in multimodal data, even with dependencies.
This work analyzes batch MARL with networked agents, providing finite-sample bounds.
problem Understanding the theoretical foundation of decentralized batch MARL with networked agents.
method Developed batch MARL algorithms for two settings: collaborative and competitive networks, without a central controller.
result Quantified finite-sample errors of estimated action-value functions for both settings.
Study real line subbundles on curves, extending classical work.
problem Understanding real line subbundles in real bundles on curves.
method Application of Atiyah's techniques and work of Lange-Narasimhan.
result Describes the Galois action on the set of lines through a real point in the moduli space of such bundles.
New algorithms reduce collaborative PAC learning sample complexity.
problem Collaborative PAC learning with reduced sample complexity.
method Design of new algorithms for both realizable and non-realizable settings.
result Sample complexity is O(ln(k)) times the worst-case sample complexity for learning a single task. Finding simpler models is often hard, but this work introduces a new tool to check if they might exist.
problem Finding accurate yet simple models is NP-hard and often not known to exist.
method Introducing the Rashomon ratio to gauge simplicity and check for the existence of simple models.
result The Rashomon ratio can help determine if a simpler model might exist before searching for it.
SCHA-VAE generates novel data from limited examples using hierarchical context aggregation.
problem Generating data from a novel distribution with limited examples.
method Hierarchical context aggregation with attention-based point to set-level aggregation.
result Hierarchical approach better captures intrinsic variability in small data.
New algorithm for ML models in gradually adapting data settings.
problem Training models when data distribution reacts to the model over time.
method Stateful Performative Gradient Descent (Stateful PerfGD)
result Stateful PerfGD minimizes performative loss in gradually adapting data settings.
Peaking phenomenon in semi-supervised learning observed and explained.
problem The peaking phenomenon in semi-supervised learning.
method Simulation studies and approximation of the learning curve.
result The learning curve in semi-supervised learning has a steeper incline and a more gradual decline.
Support vector machine (SVM) training is an active research area since the dawn of the method. In recent years there has been increasing interest in specialized solvers for the important case of linear models. The algorithm presented by Hsieh et al., probably best known under the name of the "liblinear" implementation,…
Asymmetric expansion preserves convexity in hyperbolic geometry.
problem Maintaining convexity in hyperbolic geometry under asymmetric expansions.
method Generalizing earlier results on radial expansion to asymmetric expansion.
result Asymmetric expansion of hyperbolic convex sets remains convex.
In an earlier work joint with X. X. Chen and G. Tian, we introduced the weak Kähler-Ricci flow for various geometric motivations. In the current work, we take further consideration on setting up the weak flow. Namely, the initial class is allowed to be no longer Kähler.
New algorithm achieves small-loss bounds in online learning with improved rates.
problem Achieving strong stability in online learning algorithms.
method Introduces ρ-separation to enforce strong stability, unifying previous approaches. result Oracle-efficient algorithm achieves small-loss bounds with improved rates.
Paper extends Brouwer Fixed Point Theorem with amiable and almost amiable fixed sets.
problem Extending the Brouwer Fixed Point Theorem to approximate fixed sets.
method Introducing shape boundary regions in CW spaces as amiable and almost amiable fixed subsets of dpc maps.
result Variation of Jordan Curve Theorem and Fixed Cell Complex Theorem.
New bounds on efficiency for conformalized regression methods.
problem Efficiency of conformal prediction in regression models.
method Non-asymptotic bounds on prediction set length for conformalized quantile and median regression.
result Identifies phase transitions in convergence rates across different regimes of miscoverage level.
New algorithm for duelling bandits with weak regret in adversarial settings.
problem Improving performance in duelling bandits with weak regret.
method Developed an algorithm for duelling bandits in adversarial environments, considering the Borda winner.
result Algorithm provides theoretical guarantees in both utility-based and unrestricted settings.