Generative Adversarial Networks align manifold geometries instead of densities.
problem Aligning data manifolds between domains.
method Introduces MGM GAN with importance sampling and geometry penalty.
result Advantages of modeling manifold geometry over density.
Study the distribution for low-rank matrix learning, improving inference methods.
problem Lack of understanding of underlying probability distributions in low-rank matrix learning.
method Analyze the distribution f(X)∝e−λ∥X∥∗, using differential geometry to design an improved MCMC algorithm and learn penalty parameter λ. result Improved MCMC algorithm and penalty parameter learning for low-rank Bayesian inference.
A geometric theory explains loss functions for robust representation learning.
problem Treats robustness, domain adaptation, and sensor drift as separate literatures.
method Estimates covariance Sigma_task and uses it to pin Jacobian penalties.
result Proves optimality and necessity of range coverage for penalty matrices.
Unified framework for fair regression in aware and unaware settings.
problem Lack of principled methods for fair regression in unawareness settings.
method Formulated as an optimal transport problem, unifying aware and unaware settings.
result Characterizes optimal prediction functions via optimal transport maps under different penalties.
Paper calculates the exact error of LDA models.
problem Bayesian generalization error in Latent Dirichlet Allocation (LDA).
method Theoretical analysis of learning coefficient using algebraic geometry.
result Exact asymptotic form of LDA's generalization error.
The paper explores nonconvex penalties for deep learning regularization.
problem Overfitting in deep learning neural networks.
method Examines and evaluates nonconvex penalties for DNN regularization.
result Nonconvex penalties, under certain conditions, can perform well in DNNs.
Quantum complexity lowerbound proved using differential geometry.
problem Proving lower bounds on quantum complexity.
method Applied the Bishop-Gromov bound to Nielsen's complexity geometry.
result Lower bounds on quantum complexity are exponentially large.
Gradient penalty improves GAN performance by inducing a large-margin classifier.
problem Improving GAN performance and addressing vanishing gradients.
method A unifying framework of expected margin maximization, showing gradient penalties induce large-margin classifiers.
result Gradient penalties reduce vanishing gradients and produce better generated outputs.
Study examines insider trading with penalties, finding optimal penalties increase quickly for small orders.
problem Analyzing the impact of penalties on insider trading behavior and market efficiency.
method Formal economic model with penalty functions, existence and uniqueness theorems, and optimization.
result Optimal penalties increase quickly for small orders, signaling extreme events and incorporating information into prices.
One-bit measurements widely exist in the real world, and they can be used to recover sparse signals. This task is known as the problem of learning halfspaces in learning theory and one-bit compressive sensing (1bit-CS) in signal processing. In this paper, we propose novel algorithms based on both convex and nonconvex s…
The paper studies robust risk measures with linear penalties under uncertain distributions.
problem Risk measurement under distributional uncertainty.
method Robust distortion risk measures with linear penalty function under distributional constraints.
result Explicit characterization of optimal quantile distribution and value function.
The use of machine-learning in neuroimaging offers new perspectives in early diagnosis and prognosis of brain diseases. Although such multivariate methods can capture complex relationships in the data, traditional approaches provide irregular (l2 penalty) or scattered (l1 penalty) predictive pattern with a very limited…
Paper introduces a new SVR model using a combined reward and penalty loss function.
problem Regression problem, particularly handling data points outside and inside ε-tube.
method Combined reward cum penalty loss function to penalize and reward data points.
result Experimental results support the model's properties and effectiveness.
New sparse penalty improves biclustering for gene expression data.
problem Identifying significant clusters in gene expression data.
method Prenet penalty applied to SSVD for biclustering.
result Mixed Prenet penalty effectively clusters non-overlapped data.
New approach avoids excess empirical risk in domain generalization.
problem Learning models that generalize to unseen distributions from diverse data sets.
method Minimizes penalty under constraint of optimal empirical risk, leveraging rate-distortion theory.
result Significant improvements in domain generalization performance across multiple methods.
We study the problem of estimating high-dimensional regression models regularized by a structured sparsity-inducing penalty that encodes prior structural information on either the input or output variables. We consider two widely adopted types of penalties of this kind as motivating examples: (1) the general overlappin…
Curvature penalties improve interpretability of KANs without sacrificing accuracy.
problem Pathologically high-curvature oscillations in KANs activations make them hard to interpret.
method Derived a curvature penalty and proved an upper bound on model curvature.
result KANs with curvature penalties achieve substantially smoother activations while maintaining accuracy.
New method reduces bias in sparse Bayesian learning.
problem High sparsity in statistical models leads to significant bias.
method Variable-coefficient ℓ1 penalty with hyperpriors. result Reduces bias in sparse Bayesian learning.
PPO-B improves sampling efficiency by using a logarithmic barrier method.
problem Low sampling efficiency in PPO due to exterior penalty method.
method Introducing a surrogate objective with interior penalty method.
result PPO-B outperforms PPO in terms of sampling efficiency.
New nonconvex penalty smooths at origin for deep learning.
problem Improving variable selection and bias in high-dimensional statistical learning.
method Developed a new nonconvex penalty function smooth at origin.
result Asymptotic bias of new penalty function vanishes exponentially fast.
This study proves local stability of SGP μ-WGAN and shows penalizing data or sample manifold is key.
problem Stabilizing and regularizing WGAN with gradient penalty.
method Proves local stability of SGP μ-WGAN using measure valued differentiation.
result Penalizing data or sample manifold is key to regularizing WGAN.
Physics: Similar long-distance properties can mask vastly different short-distance metrics.
problem Classifying homogeneous metrics on group manifolds by long-distance properties.
method Apply universality concept to geometry, focusing on metrics on Lie groups.
result Many metrics on low-dimensional Lie groups have similar long-distance properties despite differing short-distance properties.
We study the problem of learning high dimensional regression models regularized by a structured-sparsity-inducing penalty that encodes prior structural information on either input or output sides. We consider two widely adopted types of such penalties as our motivating examples: 1) overlapping group lasso penalty, base…
Multi-group learners suffer a penalty in transductive learning.
problem The penalty on multi-group learners in transductive learning.
method Analyzing the relationship between the number of groups and the error rate.
result The penalty can increase linearly with the number of groups, up to the square-root of the sample size.
Global minima found for multidimensional scaling with penalties.
problem Finding global minima in multidimensional scaling.
method Combining stress loss function with a quadratic penalty term to find minimizers.
result Trajectory of minimizers leads to global minima.
New method improves signal reconstruction with nonconvex penalties and parameter control.
problem Reconstructing sparse signals with nonconvex penalties and nonconvexity control.
method Introduces nonconvex penalties (SCAD, MCP) with nonconvexity parameters and controls them to guide AMP trajectory.
result Achieves perfect reconstruction for relatively dense signals with small nonconvexity parameters.
Improved penalty-based methods for bilevel optimization with reduced complexity.
problem Suboptimal complexity in solving bilevel optimization problems with large penalty terms.
method Novel penalty reformulation that decouples upper and lower-level variables, enabling larger step sizes and reduced iteration complexity.
result PBGD-Free algorithm that avoids inner loops for coupled constraint BLO problems, with reduced iteration complexity.
Proposes an alternative invariance penalty to address domain generalization issues.
problem Addressing domain generalization problems by finding invariant representations.
method Revisits the Gramian matrix of the data representation to propose an alternative invariance penalty.
result The proposed approach guarantees recovery of an invariant representation under mild conditions.
Paper proposes efficient algorithms for designing SLOPE penalty sequences.
problem Designing SLOPE penalty sequences is computationally expensive.
method Developed two efficient algorithms: PGD and CD for Gaussian and general data matrices respectively.
result Demonstrated improved mean squared error performance of SLOPE with designed penalties.
Insider trading is reduced when penalized, affecting expected penalties in a non-monotone way.
problem Reducing insider trading behavior when insiders face legal penalties.
method Characterized via a backward stochastic differential equation (BSDE) with a non-linear operator.
result The insider's expected penalties are non-monotone in the fee structure and determined by relative entropy.
Survey on minimal penalty algorithms and slope heuristics.
problem Choosing optimal multiplicative constants from data.
method Minimal penalty and slope heuristics approach.
result Slope heuristics performs almost as well as residual-based estimators.
Sparse reconstruction approaches using the re-weighted l1-penalty have been shown, both empirically and theoretically, to provide a significant improvement in recovering sparse signals in comparison to the l1-relaxation. However, numerical optimization of such penalties involves solving problems with l1-norms in the ob…
In high-dimensional and/or non-parametric regression problems, regularization (or penalization) is used to control model complexity and induce desired structure. Each penalty has a weight parameter that indicates how strongly the structure corresponding to that penalty should be enforced. Typically the parameters are c…
Improved online penalty selection for time series models.
problem Efficiently selecting penalty parameters for lasso in time series models.
method Enhanced autoregressive model with online penalty selection.
result Significantly improved computational performance and forecast accuracy.
In the multiple changepoint setting, various search methods have been proposed which involve optimising either a constrained or penalised cost function over possible numbers and locations of changepoints using dynamic programming. Such methods are typically computationally intensive. Recent work in the penalised optimi…
Nonconvex penalty methods for sparse modeling in linear regression have been a topic of fervent interest in recent years. Herein, we study a family of nonconvex penalty functions that we call the trimmed Lasso and that offers exact control over the desired level of sparsity of estimators. We analyze its structural prop…
Bayesian priors and penalties are equivalent in variational inference.
problem Understanding the relationship between Bayesian priors and penalties in variational inference.
method Characterizing the regularizers that can arise in variational inference and providing a systematic way to compute the prior corresponding to a given penalty.
result Equivalence between Bayesian priors and penalties in variational inference.
Proposes using MLP for predicting optimal penalty in changepoint detection.
problem Predicting optimal penalty for changepoints in sequences.
method Uses a multilayer perceptron (MLP) with ReLU activation function to predict penalty.
result Improves accuracy and F1 score compared to existing models.
Recently, there has been focus on penalized log-likelihood covariance estimation for sparse inverse covariance (precision) matrices. The penalty is responsible for inducing sparsity, and a very common choice is the convex l1 norm. However, the best estimator performance is not always achieved with this penalty. The …
A new penalty-free method optimizes portfolios without quantum annealing penalties.
problem Optimizing portfolios with quantum annealing penalties.
method Removing the penalty term and using a classical feasibility projector.
result Significant reduction in chain-break fractions and post-processed regret.
A new optimization scheme tackles convex objectives with non-separable penalties.
problem Optimizing convex objectives with non-separable penalties.
method Expectation-consistent approximation and vector approximate message-passing (VAMP) algorithm.
result Faster convergence compared to state-of-the-art approaches in tasks like classification and reconstruction.
Study ablated data augmentation techniques and their mathematical equivalence to penalties.
problem Lack of mathematical understanding of differences between ablated data augmentation techniques.
method Formal model of mean ablated data augmentation and inverted dropout for linear regression; empirical validation for deep networks.
result Ablated data augmentation and inverted dropout are mathematically equivalent to penalties in optimization.
Faster, better sparse model estimation for large datasets.
problem Sparse model estimation for large datasets with millions of samples and features.
method Coordinate descent, working sets, Anderson acceleration.
result Significantly faster and more efficient than state-of-the-art algorithms.
A fast method estimates group-adaptive elastic net penalties using co-data.
problem Computational inefficiency in estimating group-adaptive elastic net penalties.
method Derive low-dimensional representation of Taylor approximation for marginal likelihood and its derivative for group-adaptive ridge penalties; approximate elastic net marginal likelihood by ridge; transform ridge penalties to elastic net penalties.
result Significantly decreases computation time and outperforms other methods.
Support vector machines (SVMs) with sparsity-inducing nonconvex penalties have received considerable attentions for the characteristics of automatic classification and variable selection. However, it is quite challenging to solve the nonconvex penalized SVMs due to their nondifferentiability, nonsmoothness and nonconve…
This work addresses the issue of large covariance matrix estimation in high-dimensional statistical analysis. Recently, improved iterative algorithms with positive-definite guarantee have been developed. However, these algorithms cannot be directly extended to use a nonconvex penalty for sparsity inducing. Generally, a…
Paper develops algorithms for sparse linear regression with generalized elastic net penalty.
problem Sparse linear regression with robust penalty for high-dimensional data.
method Iterative Reweighted Framework based on ADMM and PMM with SNN.
result Efficient algorithms provide superior performance in both simulated and real data.
We consider a class of constrained optimization problems with a possibly nonconvex non-Lipschitz objective and a convex feasible set being the intersection of a polyhedron and a possibly degenerate ellipsoid. Such problems have a wide range of applications in data science, where the objective is used for inducing spars…