In this paper, we study the Nystr{ö}m type subsampling for large scale kernel methods to reduce the computational complexities of big data. We discuss the multi-penalty regularization scheme based on Nystr{ö}m type subsampling which is motivated from well-studied manifold regularization schemes. We develop a theoretica…
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48 results for “penalty schemes”
A Penalty Method for the Numerical Solution of Hamilton-Jacobi-Bellman (HJB) Equations in Financeq-fin.CP
We present a simple and easy to implement method for the numerical solution of a rather general class of Hamilton-Jacobi-Bellman (HJB) equations. In many cases, the considered problems have only a viscosity solution, to which, fortunately, many intuitive (e.g. finite difference based) discretisations can be shown to co…
We introduce an iterative optimization scheme for convex objectives consisting of a linear loss and a non-separable penalty, based on the expectation-consistent approximation and the vector approximate message-passing (VAMP) algorithm. Specifically, the penalties we approach are convex on a linear transformation of the…
Generative diffusion models forecast implied vol surfaces without arbitrage issues.
problem Forecasting arbitrage-free implied volatility surfaces using historical data with path-dependent dynamics.
method Generative diffusion model (DDPM) with conditional training on market variables, including EWMAs and returns. Dynamic penalty scheme based on SNR to enforce arbitrage-free surfaces.
result Superior performance in volatility forecasting compared to existing methods.
Paper solves convertible bond valuation using finite elements with penalty method.
problem Valuation of convertible bonds under penalty TF model.
method Solves TF system of equations using P1 and P2 finite elements with penalty method.
result Numerical solutions compare favorably with finite difference method.
This paper proposes a new interpretation of sparse penalties such as the elastic-net and the group-lasso. Beyond providing a new viewpoint on these penalization schemes, our approach results in a unified optimization strategy. Our experiments demonstrate that this strategy, implemented on the elastic-net, is computatio…
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…
Paper proposes SMO for solving bilevel optimization problems efficiently.
problem Solving bilevel optimization problems with nonsmooth convex lower-level and nonconvex upper-level objectives.
method Sequential minimax optimization (SMO) method using modified augmented Lagrangian and penalty schemes.
result Improves operation complexity for finding -KKT solutions.
Paper proposes a method to improve circular coordinate representation for detecting changes in high-dimensional datasets.
problem Detecting changes in high-dimensional datasets with preserved topological structures.
method Adapt circular coordinate framework using a generalized penalty function instead of an L2 penalty.
result Circular coordinates with generalized penalty can detect changes in high-dimensional datasets under different sampling schemes.
Gradient descent training of neural networks leads to solutions close to natural cubic splines.
problem Understanding the implicit bias of gradient descent in neural networks.
method Analysis of gradient descent training for wide neural networks, focusing on the curvature penalty and initialization schemes.
result The solutions of gradient descent training are polyharmonic splines for certain initialization schemes.
Systematic trading strategies are rule-based procedures which choose portfolios and allocate assets. In order to attain certain desired return profiles, quantitative strategists must determine a large array of trading parameters. Backtesting, the attempt to identify the appropriate parameters using historical data avai…
We consider the l1-regularized Markowitz model, where a l1-penalty term is added to the objective function of the classical mean-variance one to stabilize the solution process, promoting sparsity in the solution. The l1-penalty term can also be interpreted in terms of short sales, on which several financial markets hav…
Insiders camouflage trading to balance wealth and stealth, avoiding legal penalties.
problem Legal penalties and insider trading among liquidity traders.
method Kyle-type model with a diverse spectrum of prosecution schemes.
result Existence and uniqueness of equilibria for large populations, with a stealth index revealing trading scale.
A new insurance and reinsurance pricing scheme based on realized loss.
problem Determining fair and risk-adjusted insurance premiums.
method Performance-based variable premium scheme with random initial premium adjusted based on realized loss.
result The variable premium scheme reduces reinsurer's total risk exposure compared to expected-value premium.
Operator splitting schemes for American options under the two-asset Merton jump-diffusion modelmath.NA
This paper deals with the efficient numerical solution of the two-dimensional partial integro-differential complementarity problem (PIDCP) that holds for the value of American-style options under the two-asset Merton jump-diffusion model. We consider the adaptation of various operator splitting schemes of both the impl…
Single deep model detects out-of-distribution data with single forward pass.
problem Detecting out-of-distribution data points in neural networks.
method Deterministic uncertainty quantification (DUQ) using gradient penalty for reliable detection.
result Single model outperforms or matches ensemble methods in out-of-distribution detection.
Convergence analysis of Tikhonov regularization for non-linear statistical inverse learning problemsmath.ST
We study a non-linear statistical inverse learning problem, where we observe the noisy image of a quantity through a non-linear operator at some random design points. We consider the widely used Tikhonov regularization (or method of regularization, MOR) approach to reconstruct the estimator of the quantity for the non-…
GTMs model complex multivariate data with varying conditional independencies.
problem Modeling multivariate data with intricate marginals and complex dependency structures.
method Semiparametric approach using penalized splines and lasso regularization.
result GTMs accurately learn complex dependencies and identify conditional independencies.
We consider the problem of estimating a sparse multi-response regression function, with an application to expression quantitative trait locus (eQTL) mapping, where the goal is to discover genetic variations that influence gene-expression levels. In particular, we investigate a shrinkage technique capable of capturing a…
Sparse optimization refers to an optimization problem involving the zero-norm in objective or constraints. In this paper, nonconvex approximation approaches for sparse optimization have been studied with a unifying point of view in DC (Difference of Convex functions) programming framework. Considering a common DC appro…
A Stable Lassostat.ME
Improves Lasso's stability in correlated predictor settings.
problem Lasso's selection stability deteriorates with correlated predictors.
method Integrates a weighting scheme into the Lasso penalty function, using a correlation-adjusted ranking.
result Demonstrates improved selection stability on simulated and real-world datasets.
PAIR optimizes machine learning models to generalize better to out-of-distribution data.
problem Optimization of machine learning models for out-of-distribution (OOD) generalization often leads to compromises that weaken robustness.
method Introduces a multi-objective optimization (MOO) perspective and a new optimization scheme called PAreto Invariant Risk Minimization (PAIR).
result PAIR improves robustness of OOD objectives by cooperatively optimizing with other objectives, yielding top OOD performances.
New methods tackle statistical inverse problems with random data.
problem Statistical inverse problems with random experimental design.
method Spectral regularization, regularization by projection, convex penalties.
result Minimax rates in expectation and probability for convergence.
Regularization methods are often employed in deep learning neural networks (DNNs) to prevent overfitting. For penalty based DNN regularization methods, convex penalties are typically considered because of their optimization guarantees. Recent theoretical work have shown that nonconvex penalties that satisfy certain reg…
Quantum Proof-of-Work uses boson sampling to secure blockchain consensus.
problem Ensuring secure and efficient blockchain consensus.
method Proposes using quantum boson sampling as a Proof-of-Work scheme for blockchain.
result Demonstrates a robust and energy-efficient PoW scheme.
Deep weight factorization improves neural network training through smooth optimization of sparse penalties.
problem Challenges in applying sparse regularization in neural networks due to non-differentiability of penalties.
method Introduces deep weight factorization, decomposing weights into multiple factors for smooth optimization of -penalized networks.
result Deep weight factorization outperforms shallow factorization and pruning methods consistently across various architectures and datasets.
Study benchmarks methods for learning non-Cartesian k-space trajectories and reconstruction.
problem Benchmarking methods for learning non-Cartesian k-space trajectories and reconstruction.
method Comparing PILOT, BJORK, and HybLearn schemes to learn non-Cartesian k-space trajectories and reconstruction.
result HybLearn scheme outperforms other methods in learning and comparing non-Cartesian k-space trajectories and reconstruction.
In the setting of high-dimensional linear regression models, we propose two frameworks for constructing pointwise and group confidence sets for penalized estimators which incorporate prior knowledge about the organization of the non-zero coefficients. This is done by desparsifying the estimator as in van de Geer et al.…
This paper deals with sparse feature selection and grouping for classification and regression. The classification or regression problems under consideration consists in minimizing a convex empirical risk function subject to an constraint, a pairwise constraint, or a pairwise constraint. …
Gradient-based method prunes large models to create transferable architectures.
problem Creating transferable architectures from large models with limited fine-tuning data.
method Gradient-based algorithm for architecture pruning and subset selection.
result Successfully retrain architectures on new tasks with few fine-tuning data.
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…
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.
Motivated by applications in hyperspectral imaging we investigate methods for approximating a high-dimensional non-negative matrix by a product of two lower-dimensional, non-negative matrices and This so-called non-negative matrix factorization is based…
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…
A popular heuristic for improved performance in Generative adversarial networks (GANs) is to use some form of gradient penalty on the discriminator. This gradient penalty was originally motivated by a Wasserstein distance formulation. However, the use of gradient penalty in other GAN formulations is not well motivated.…
Study uses FEM for HJB in option pricing with borrowing fees, improving accuracy and efficiency.
problem Optimal control problems in financial markets with frictions.
method Finite element method with non-uniform mesh, theta-scheme time integration, Newton-type algorithm.
result Efficient and accurate solution to HJB equation for option pricing with borrowing fees.
Clusterpath estimator simplifies graphical model interpretation for large datasets.
problem Difficulty in interpreting graphical models with many variables.
method Clusterpath estimator that groups variables for block-structured precision matrix.
result CGGM outperforms other methods in variable clustering and practical applications.
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 penalty with hyperpriors.
result Reduces bias in sparse Bayesian learning.
2D-PT improves sampling in constrained optimization problems.
problem Sampling Boltzmann distributions with soft constraints.
method Two-dimensional extension of parallel tempering.
result 2D-PT achieves near-ideal mixing in constrained problems.
Insider Trading with Penaltiesq-fin.TR
We consider a one-period Kyle (1985) framework where the insider can be subject to a penalty if she trades. We establish existence and uniqueness of equilibrium for virtually any penalty function when noise is uniform. In equilibrium, the demand of the insider and the price functions are in general non-linear and remai…
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.
In this paper, we develop a variant of the well-known Gauss-Newton (GN) method to solve a class of nonconvex optimization problems involving low-rank matrix variables. As opposed to the standard GN method, our algorithm allows one to handle general smooth convex objective function. We show, under mild conditions, that …
We methodologically address the problem of Q-value overestimation in deep reinforcement learning to handle high-dimensional state spaces efficiently. By adapting concepts from information theory, we introduce an intrinsic penalty signal encouraging reduced Q-value estimates. The resultant algorithm encompasses a wide r…
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…