Non-convex regularizers usually improve the performance of sparse estimation in practice. To prove this fact, we study the conditions of sparse estimations for the sharp concave regularizers which are a general family of non-convex regularizers including many existing regularizers. For the global solutions of the regul…
Noise regularization improves CDE models without overfitting.
problem Overfitting in neural network-based conditional density estimation.
method Noise regularization method that adds random perturbations to data.
result Noise regularization significantly outperforms other methods across various datasets and models.
The study finds necessary and sufficient conditions for C1-hypersurfaces to have nowhere C1-regular parallel sets.
problem Conditions for C1-hypersurfaces to have nowhere C1-regular parallel sets. method Proves a necessary and sufficient condition for C1-hypersurfaces to have nowhere C1-regular parallel sets. result A necessary and sufficient condition for C1-hypersurfaces to have nowhere C1-regular parallel sets. Verifies regularity for conditional expectation operators and embeddings, simplifying validation.
problem Characterizing when conditional expectation operators map between function spaces.
method Establishes a verifiable sufficient condition for bounded and Hilbert-Schmidt mappings based on conditional density regularity.
result Averifiable condition for mapping properties of conditional expectation operators simplifies validation.
This paper investigates how policy conditioning affects reinforcement learning stability.
problem Improving stability and generalization of reinforcement learning agents.
method The authors study Jacobian conditioning behavior during policy optimization and propose a conditioning regularization algorithm.
result The proposed conditioning regularization algorithm enhances reinforcement learning agent generalization.
The paper explores ρ-regularity for real analytic maps and its relation to Milnor fibrations.
problem Understanding the conditions for ρ-regularity in analytic map germs. method Analyzes Thom regular stratifications and Milnor condition (b) for germs of analytic maps.
result Thom regular stratifications and Milnor condition (b) are crucial for ρ-regularity and open book structures. Regular representation of measures on manifolds with boundary.
problem Representing probability densities on manifolds near boundaries.
method Sufficient conditions for Ck random maps, obstructions to representability. result Conditions for regular representation of measures near boundaries.
Classifies local boundary conditions for Dirac-type operators on manifolds.
problem Determining all local smooth boundary conditions for Dirac-type operators.
method Combining general theory of boundary value problems for Dirac operators and pointwise considerations.
result Classification of local self-adjoint regular boundary conditions for Dirac spinors in dimensions 3 and 4.
Uniform Shapiro-Lopatinski conditions ensure well-posedness of boundary value problems on manifolds with bounded geometry.
problem Boundary value problems on manifolds with boundary and bounded geometry.
method Uniform Shapiro-Lopatinski regularity condition, compactness argument, Nirenberg trick.
result Uniform Shapiro-Lopatinski condition characterizes well-posed boundary value problems.
Paper introduces a differentiable regularizer for condition number to improve neural network stability.
problem Maintaining numerical stability in neural networks to ensure reliable and performant models.
method Introduces a novel differentiable regularizer for the condition number of weight matrices.
result Derives a differentiable formula for the gradient of the regularizer, promoting matrices with low condition numbers.
Proposes a new method for selecting regularization parameters in sparse precision matrix estimation.
problem Selecting an appropriate regularization parameter for sparse precision matrix estimation.
method Developed a closed-form matrix-valued regularization parameter based on the sampling distribution of optimality conditions.
result The proposed method achieves comparable estimation accuracy and superior support recovery to cross-validation, with significant runtime improvements.
The paper analyzes Tikhonov regularization in Hilbert scales for statistical inverse problems.
problem Statistical inverse problems in Hilbert scales with general noise.
method Tikhonov regularization scheme with conditional stability estimates and high probability error bounds.
result Explicit rates of convergence for oversmoothing and regular cases over defined regularity classes.
Derives spacetime regularity under specific curvature conditions.
problem Ensuring smoothness in spacetime models with given curvature constraints.
method General regularity estimate for 4-d spacetimes, using Ricci curvature and Lie derivatives.
result Establishes conditions for smoothness in spacetime models.
Proposes a method to generate diverse outputs in conditional GANs.
problem Mode-collapse in conditional GANs, where outputs are overly simplified.
method Explicit regularization to produce diverse outputs based on latent codes.
result Demonstrates improved diversity in image-to-image translation, inpainting, and future video prediction tasks.
Study on optimal rates for learning algorithms with polynomial eigenvalue decay.
problem Understanding convergence rates of learning algorithms under general source conditions.
method Analyzes Tikhonov regularization and operator monotone index functions in minimax setting.
result Establishes upper convergence rates and minimum possible error for learning algorithms.
A regular F-manifold is an F-manifold (with Euler field) (M, \circ, e, E), such that the endomorphism {\mathcal U}(X) := E \circ X of TM is regular at any p\in M. We prove that the germ ((M,p), \circ, e, E) is uniquely determined (up to isomorphism) by the conjugacy class of {\mathcal U}_{p} : T_{p}M \rightarrow T_{p}M…
Real analytic maps prove fibration on spheres and tubes with regularity condition.
problem Understanding fibration properties of real analytic maps with isolated critical points/values.
method Proving fibration properties using (m)-regularity condition.
result Real analytic maps with isolated critical points/values are fibrations on small spheres and tubes.
Equivalence found between algorithmic regularization and convex penalization for convex losses.
problem Understanding the relationship between algorithmic regularization and convex penalization.
method Introducing a geometric condition and showing equivalence through optimization paths.
result Optimization paths of iterative algorithms on unregularized problems match those of corresponding penalized problems under certain conditions.
IRKSN algorithm achieves sparse recovery with wider applicability conditions.
problem Sparse recovery challenges due to NP-hard nature and restrictive conditions.
method IRKSN algorithm based on k-support norm regularizer. result Achieves sparse recovery with explicit constants and standard linear rate.
Unified framework for understanding and optimizing training acceleration.
problem Challenges in optimizing training with regularization and acceleration techniques.
method Explains how AdaGrad, RMSProp, and Adam accelerate training, and derives a generalization for L1-regularization. result Derives a unified mathematical framework for understanding and optimizing training acceleration.
The paper extends completeness notions to low-regularity spacetimes.
problem Defining completeness conditions for spacetimes with low-regularity metrics.
method Extending Beem's completeness notions to Lorentzian length spaces and proving relationships between them.
result Equivalence of completeness conditions for globally hyperbolic C1-spacetimes under certain conditions. The study shows that certain graphs are regular at boundary points.
problem Boundary regularity of anisotropic minimal Lipschitz graphs.
method Proves regularity for graphs with bounded anisotropic mean curvature and atomic energy condition.
result Regularity at boundary points with density bounded above by 1/2 + σ.
In this paper we prove that every definable set has a definable triangulation which is locally Lipschitz and weakly bi-Lipschitz on the natural simplicial stratification of the simplicial complex. We also distinguish a class T of regularity conditions and give a universal construction of a definable triangulation with …
In this paper we describe the notion of a weak lipschitzianity of a mapping on a Cq stratification. We also distinguish a class of regularity conditions that are in some sense invariant under definable, locally Lipschitz and weakly bi-Lipschitz homeomorphisms. This class includes the Whitney (B) condition and the …
Proposes SHADE, a new regularization scheme for deep learning.
problem Improving classification performance in deep learning.
method SHADE uses information theory to define a prior based on conditional entropy, decoupling representation learning from data fitting.
result Empirically validated improvements over standard regularization schemes.
Proposes SHADE, a new regularization scheme for deep learning.
problem Improving classification performances in deep learning.
method SHADE uses information theory to define a prior based on conditional entropy, decoupling representation learning from data fitting.
result Empirically validated improvements over common regularization schemes.
This paper studies least-square regression penalized with partly smooth convex regularizers. This class of functions is very large and versatile allowing to promote solutions conforming to some notion of low-complexity. Indeed, they force solutions of variational problems to belong to a low-dimensional manifold (the so…
New method for estimating global and local parameters using regularized Riesz representers.
problem Estimating global and local parameters in complex models robustly.
method Adaptive inference methods based on ℓ1 regularization, including Riesz representer as a nuisance parameter.
result Non-asymptotic and asymptotic uniform validity for honest confidence bands.
Curvature formulas on regular graphs identified bone idle edges and graphs.
problem Understanding curvature in regular graphs and identifying bone idle edges.
method Explicit formulas for Lin-Lu-Yau and Ollivier-Ricci curvatures derived from graph parameters.
result Equality condition on regular graphs for Ollivier-Ricci curvature and characterization of bone idle edges.
New learning rates derived for Tikhonov-regularized problems without kernel assumptions.
problem Learning rates for Tikhonov-regularized learning problems.
method Minimax adaptive rates derived using Fourier isocapacitary condition and interpolation theory.
result Derivation of minimax adaptive rates without requiring kernel assumptions.
In this work, we study data preconditioning, a well-known and long-existing technique, for boosting the convergence of first-order methods for regularized loss minimization. It is well understood that the condition number of the problem, i.e., the ratio of the Lipschitz constant to the strong convexity modulus, has a h…
Introduces REVE, a regularization scheme that compresses class conditioned entropy.
problem Improving generalization performance of deep learning models.
method Identifies a variable responsible for final prediction, compresses class conditioned entropy, introduces a variational upper bound, and integrates a tractable loss into training.
result Demonstrates the efficiency of REVE on various neural networks and datasets.
Curve shortening flow's regularity depends on initial conditions after a certain time.
problem Understanding the regularity of evolving curves under curve shortening flow.
method Proposing and proving principles of controllable regularity based on initial conditions.
result No regularity estimate holds before a specific time, A/π. The aim of this note is to present an alternative proof for an already known result relative to the solvability of the Dirichlet problem in Riemannian manifolds (see remark 0.1). In particular, we discuss the p-regularity (regularity relative to the p-laplacian) of domains of the form I = O-K, where O is a regular doma…
We formulate a principle for classification with the knowledge of the marginal distribution over the data points (unlabeled data). The principle is cast in terms of Tikhonov style regularization where the regularization penalty articulates the way in which the marginal density should constrain otherwise unrestricted co…
Entropy-regularized NPG converges linearly with linear function approximation.
problem Analyzing convergence of entropy-regularized NPG with function approximation.
method Established finite-time convergence analyses with entropy regularization and linear function approximation.
result Entropy-regularized NPG achieves linear convergence up to a function approximation error.
Study uses property elicitation to understand how fairness regularizers affect optimal decisions.
problem Understanding how fairness regularizers change the optimal decision in predictive algorithms.
method Property elicitation to analyze the relationship between loss, regularization, and optimal decision.
result Necessary and sufficient condition for when a property changes with the addition of a regularizer.
The paper defines conditions for Gaussian process sample path regularity.
problem Lack of understanding of Gaussian process sample path regularity.
method Analyzes covariance kernels to determine sample path regularity.
result Necessary and sufficient conditions for Hölder regularity are provided.
Conditional Asian options are recent market innovations, which offer cheaper and long-dated alternatives to regular Asian options. In contrast with payoffs from regular Asian options which are based on average asset prices, the payoffs from conditional Asian options are determined only by average prices above certain t…
Unified framework for estimating high-dimensional conditional factor models.
problem Estimating high-dimensional conditional latent factor models with practical limitations.
method Constrained nuclear norm regularization and cross-validation for parameter selection.
result Imposing homogeneity improves model predictability, with new method outperforming alternatives.
Study conical Kaehler-Einstein metrics' curvature, proving regularity and geometric conditions.
problem Curvature of conical Kaehler-Einstein metrics on Kaehler manifolds.
method Proved regularity for Monge-Ampère equations on Kaehler manifolds with smooth divisors, applied to conical metrics.
result Geometric condition for boundedness of conical singularities.
The paper tackles safe reinforcement learning with convex regularization.
problem Safe reinforcement learning in complex, high-dimensional settings with safety constraints.
method Doubly-regularized RL framework combining reward and parameter regularization, formulated as a convex regularized objective with parametrized policies on an infinite-dimensional statistical manifold.
result Exponential convergence guarantees under sufficient regularization, robust theoretical insights and guarantees for safe RL.
New method for fitting graphical models with latent variables using regularized conditional likelihood.
problem Graphical modeling with latent variables and confounding dependencies.
method Regularized conditional likelihood for exponential family graphical models.
result Framework applicable to broader settings without knowing latent variables' distribution.
DG algorithms often fail to generalize well in limited domains, highlighting necessary vs. sufficient conditions.
problem DG algorithms fail to consistently outperform ERM in limited domains.
method Examined necessary and sufficient conditions for DG, proposing a subspace alignment method.
result DG methods focus on sufficient conditions, often neglecting necessary conditions, leading to generalization failures.
Proposes a regularization method for Bayesian networks to improve model generalization.
problem Improving model generalization in Bayesian networks.
method Distribution-based penalization approach that encourages similar conditional probability distributions.
result Proposed method solves the wave propagation modeling problem better than baseline methods.
Proposes a framework for sparse optimal policies in reinforcement learning.
problem Finding sparse optimal policies in reinforcement learning.
method Regularized Markov decision processes (MDPs) with specific regularization terms.
result Sufficient and necessary conditions for inducing sparse optimal policies.
We study a hybrid conditional gradient - smoothing algorithm (HCGS) for solving composite convex optimization problems which contain several terms over a bounded set. Examples of these include regularization problems with several norms as penalties and a norm constraint. HCGS extends conditional gradient methods to cas…
Study Dirac operators on finite warped cylinders with gauge fields.
problem Characterize spectral flow on finite warped cylinders with gauge fields.
method Identify endpoint operators, derive determinant characterization, introduce regularized APS conditions.
result Regularized APS conditions admit a spectral-flow framework, matching zero-mode sets.