Greedy convex combination of models outperforms baselines.
problem Overfitting and underfitting in convex combinations of models.
method Greedy learning of convex combinations with early stopping.
result Greedy approach is competitive or better than boosting and random forests.
Combination theorems for convex projective geometry subgroups.
problem Understanding discrete subgroups in convex projective geometry.
method General combination theorems for discrete subgroups preserving properly convex open subsets.
result Free products of convex cocompact subgroups are convex cocompact.
New method improves Variational Auto-Encoders using convex combination of Inverse Autoregressive Flows.
problem Improving Variational Auto-Encoders (VAEs) for better performance.
method Introducing multiple lower-triangular matrices with ones on the diagonal and combining them using a convex combination to enrich a linear Inverse Autoregressive Flow.
result The proposed method outperforms other volume-preserving flows and is competitive with state-of-the-art linear normalizing flows.
This paper proves Expected Shortfall is concave, not convex.
problem Understanding the convexity/concavity of Expected Shortfall.
method Analytical proof of concavity with respect to probability distributions.
result Expected Shortfall is concave, not convex.
Linear speedup achieved in non-convex optimization for decentralized systems.
problem Achieving optimal performance in decentralized non-convex optimization.
method Examined the dependence of convergence guarantees on spectral properties of combination policies.
result Linear speedup in saddle-point escape time for symmetric combination policies.
Near-convex archetypal analysis improves interpretability and fitting error in NMF.
problem High data fitting error in traditional archetypal analysis.
method Introduces near-convex archetypal analysis (NCAA) that combines AA and NMF.
result NCAA achieves lower data fitting error than state-of-the-art methods.
Noisy Feature Mixup improves model robustness with noise-perturbed convex combinations.
problem Improving model robustness against data perturbations.
method Noise-perturbed convex combinations of pairs of data points in input and feature space.
result Improved model robustness and favorable trade-offs between accuracy and robustness.
Prototypal analysis improves archetypal analysis by penalizing distant prototypes, making it more robust and interpretable.
problem Sensitivity to outliers and non-locality in archetypal analysis limit its applicability as a learning tool.
method Prototypal analysis finds prototypes through convex combination of data points, penalizing distant prototypes.
result Prototypal analysis is more robust and interpretable than archetypal analysis.
Dual explanation method using convex hulls and example-based vectors.
problem Local and global explanation of complex models.
method Dual representation of instances as convex combinations, generating new dual dataset, training linear surrogate model, computing feature importance.
result Effective example-based and local/global explanation of complex models.
Combines machine learning and convex limiting for accurate subgrid flux modeling in shallow-water equations.
problem Accurate subgrid flux modeling in shallow-water equations.
method Machine learning and flux limiting for property-preserving subgrid scale modeling.
result The proposed method produces meaningful closures even in untrained scenarios.
Combination theorem for geodesic coarsely convex group pairs.
problem Understanding properties of groups relative to subgroups.
method Definitions of weakly semihyperbolic, semihyperbolic, and geodesic coarsely convex group pairs; combination theorem.
result Combination theorem for geodesic coarsely convex group pairs.
Estimates multiple means in high dimensions using convex combinations.
problem Estimating multiple multi-dimensional means from samples.
method Convex combinations of empirical means with data-dependent weights.
result Our methods asymptotically approach oracle (minimax) improvement.
Proposes a convex method for high-dimensional sparse sliced inverse regression.
problem Difficulty in interpreting results and variability in high-dimensional settings.
method Convex formulation and linearized alternating direction methods of multiplier algorithm.
result Upper bound on the subspace distance between estimated and true subspaces.
Study continuous paths in discrete subgroups of hyperbolic space, proving combination and decomposition theorems.
problem Understanding continuous paths in discrete subgroups of hyperbolic space.
method Combination theorem and chromatography technique.
result Construction of an exotic path of discrete subgroups with no isomorphic subgroups.
Safe neural networks for input-output specifications.
problem Ensuring machine learning models adhere to input-output constraints.
method Designing constrained predictors and combining them safely.
result Demonstrated on synthetic and real-world datasets.
We present a novel, log-radius profile representation for convex curves and define a new operation for combining the shape features of curves. Unlike the standard, angle profile-based methods, this operation accurately combines the shape features in a visually intuitive manner. This method have implications in shape an…
It is generally believed that ensemble approaches, which combine multiple algorithms or models, can outperform any single algorithm at machine learning tasks, such as prediction. In this paper, we propose Bayesian convex and linear aggregation approaches motivated by regression applications. We show that the proposed a…
The MAXVAR risk measure is shown coherent and provides a formula for its risk envelope.
problem Coherency and formula for MAXVAR risk measure.
method Elementary proof of coherency, observation of convex combination, explicit formula derivation.
result MAXVAR risk measure is coherent and has an explicit risk envelope formula.
Proves convergence of PSGLA for sampling non-convex potentials.
problem Sampling from non-convex potentials with stability.
method Combines ULA and proximal optimization with stability analysis.
result First proof of convergence for PSGLA on non-convex potentials.
A new matrix factorization method that approximates data without requiring nonnegativity or convexity.
problem Approximating data matrices without the constraints of nonnegativity or convexity.
method A multi-objective optimization problem finds conical combinations of templates that approximate a given data matrix.
result The method allows for approximation of data sets without the usual constraints of nonnegativity or convexity.
The study proves the existence of k-convex hypersurfaces for specific curvature equations.
problem Proving the existence of k-convex hypersurfaces for Hessian curvature equations. method Combining a priori estimates with the continuity method, and establishing a constant rank theorem.
result Existence and uniqueness of k-convex hypersurfaces for both nonhomogeneous and homogeneous Hessian curvature equations. Paper studies how to combine regret minimizers for solving complex games.
problem Solving large-scale extensive-form games with constraints.
method Derives a calculus for constructing regret minimizers for composite convex sets.
result Local regret minimizers for simpler sets can be combined into an aggregate for composite sets.
This paper characterizes hierarchical clustering methods that abide by two previously introduced axioms -- thus, denominated admissible methods -- and proposes tractable algorithms for their implementation. We leverage the fact that, for asymmetric networks, every admissible method must be contained between reciprocal …
New binary AA methods improve on existing techniques.
problem Binary data limitations in AA methods.
method Proposed two optimization frameworks for binary AA.
result Superior performance on synthetic and real binary data.
Optimal domain adaptation model using Fisher's Linear Discriminant.
problem Improving classification accuracy across different domains.
method Convex combination of source and target hypotheses, derived under 0-1 loss.
result Effective classifier can be computed without direct source task information.
The Extended Courant Property is disproven for certain linear combinations of eigenfunctions.
problem Disproving the Extended Courant Property for specific cases.
method Simple and explicit examples of domains (convex, with cracks, sphere, torus) are provided.
result The Extended Courant Property is not universally true for linear combinations of eigenfunctions.
The paper proves a new inequality for 3-manifolds with noncompact boundaries.
problem Proving positivity of a convex combination of ADM masses on 3-manifolds with noncompact boundaries.
method Obtained an integral inequality for asymptotically linear harmonic functions.
result Positivity of a convex combination of ADM masses under a positivity condition on scalar curvatures and boundary mean curvatures.
Defines diversification as a binary relationship between financial portfolios.
problem Defines diversification in a new binary relationship for financial portfolios.
method Proposes a new definition of diversification based on convex linear combinations and second order stochastic dominance.
result The proposed definition coincides with second order stochastic dominance.
This expository paper presents elementary proofs of four basic results concerning derivatives of quasi-convex functions. They are combined into a fifth theorem which is simple to apply and adequate in many cases. Along the way we establish the equivalence of the basic lemmas of Jensen and Slodkowski.
Pseudo-Anosov subgroups in surface bundles over tori are convex cocompact.
problem Understanding the structure of pseudo-Anosov subgroups in surface bundles over tori.
method Using the Birman exact sequence to show convex cocompactness.
result Finitely generated, purely pseudo-Anosov subgroups are convex cocompact in surface bundles over tori.
For a sequence of nonnegative random variables, we provide simple necessary and sufficient conditions to ensure that each sequence of its forward convex combinations converges in probability to the same limit. These conditions correspond to an essentially measure-free version of the notion of uniform integrability.
New algorithm improves convergence for non-convex problems with boundaries.
problem Optimizing non-convex problems with constraints.
method Reflected Gradient Langevin Dynamics with probabilistic representation.
result Promising convergence rates, faster than existing methods.
Develops a Riemannian archetypal analysis for interpretable non-linear data.
problem Limited performance of classical archetypal analysis on non-linear data.
method Riemannian geometry for data-driven pullback, geodesic convex combinations, convex relaxation followed by non-convex refinement.
result Combines interpretability of classical archetypal analysis with expressive power of modern non-linear models.
This work proposes ACTC for adaptive distributed learning under communication constraints.
problem Adaptive distributed learning in networks with communication constraints.
method ACTC (Adapt-Compress-Then-Combine) strategy with diffusion exchange of compressed updates.
result ACTC iterates converge to the optimizer with significant bit savings.
Improved kernel quadrature with convex weights using subsampling.
problem Constructing quadrature rules with small worst-case error.
method Combining spectral properties of the kernel with recombination results.
result Effective algorithms for constructing convex quadrature rules with i.i.d. samples.
AA extracts archetypes from data for clear feature extraction.
problem Non-convex optimization problem in AA.
method Computational procedure extracting archetypes as convex combinations of data.
result AA offers interpretable representations for high-dimensional data.
We prove that each non-separable completely metrizable convex subset of a Frechet space is homeomorphic to a Hilbert space. This resolves an old (more than 30 years) problem of infinite-dimensional topology. Combined with the topological classification of separable convex sets due to Klee, Dobrowoslki and Torunczyk, th…
Paper proposes Vertex Networks for reinforcement learning of control systems with safety guarantees.
problem Challenges in reinforcement learning with hard state and action constraints.
method Vertex Networks incorporate safety constraints into policy network architecture, ensuring safety during exploration.
result Proposed Vertex Networks outperform vanilla reinforcement learning in benchmark control tasks.
New algorithm combines gradient and coordinate descent steps for faster convergence.
problem Optimizing smooth convex functions over atom-spans.
method Blended matching pursuit combining coordinate descent and gradient descent.
result Derives linear convergence rates for non-strongly convex functions.
Risk-averse approach for online convex bandit problems.
problem Online convex optimization with bandit feedback for risk-averse decision makers.
method Two algorithms: descent-type and ellipsoid method-based.
result Achieves optimal regret bounds for risk-aversion.
The study finds at least 2 free-boundary minimal disks in convex 3-balls.
problem Finding minimal disks in convex 3-balls.
method Combining mean curvature flow, min-max theory, and degree theory.
result Existence of at least 2 free-boundary minimal disks in convex 3-balls for generic metrics.
Paper proposes algorithms for sparse signal estimation with nonconvex regularization.
problem Sparse signal estimation with nonconvex regularization.
method Successive convex approximation framework combining majorization-minimization and line search.
result Flexibility, fast convergence, low complexity, guaranteed convergence to stationary point.
Simple conditions for comonotonic additive risk measures from acceptance sets.
problem Conditions for comonotonic additive risk measures from acceptance sets.
method Conditions on acceptance sets for induced comonotonic additive risk measures.
result Acceptance sets induce comonotonic additive risk measures if and only if the acceptance sets and their complements are stable under convex combinations of comonotonic random variables.
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.
We introduce the moduli space of spectral curves of constant mean curvature (\cmc\hspace{-5pt}) cylinders of finite type in the round unit 3-sphere. The subset of spectral curves of mean-convex Alexandrov embedded cylinders is explicitly determined using a combination of integrable systems and geometric analysis techni…
Solves convex optimization with many constraints in a distributed system.
problem Solving convex optimization problems with many convex constraints in a distributed setting.
method Extension of ADMM to handle arbitrary inequality constraints.
result Inherits convergence guarantees of ADMM and Augmented Lagrangian method.
Uniqueness of convex self-similar solutions shown for a specific curvature flow.
problem Uniqueness of strictly convex closed self-similar solutions to the Gauss curvature flow.
method Introduced a Pogorelov type computation and applied the strong maximum principle.
result Uniqueness of strictly convex closed smooth self-similar solutions to the α-Gauss curvature flow with (1/n)<α<1+(1/n). An online convex matrix factorization algorithm with interpretable bases.
problem Scaling and interpretability in matrix factorization for large datasets.
method Online algorithm with representative data samples for interpretability.
result Significant computational savings compared to classical convex MF.