Improved guarantees for sparse random embeddings with explicit bounds and empirical superiority.
problem Improving the explicitness and sharpness of guarantees for sparse random embeddings.
method Explicit bounds, tighter estimates for quadratic chaos, extreme properties of sparse linear forms, and improved bounds for sums of independent random variables.
result Significantly outperforms prior works on various real-world datasets.
Zero loss is achievable in overparametrized DL networks under specific conditions.
problem Achieving zero loss in overparametrized deep learning networks.
method Determine sufficient conditions for zero loss attainability and present an explicit construction of zero loss minimizers.
result Explicit minimizers for zero loss in overparametrized DL networks are constructed without gradient descent.
Develops methods to analyze manifold singularities using graph Laplacian.
problem Analyzing geometric properties of singularities in datasets.
method Theory and methods using the graph Laplacian to provide explicit bounds on manifold singularities.
result Explicit bounds on the graph Laplacian for functions near manifold singularities.
In a market with stochastic volatility and jumps, we consider a VIX-linked fee structure for variable annuity contracts with guaranteed minimum withdrawal benefits (GMWB). Our goal is to assess the effectiveness of the VIX-linked fee structure in decreasing the sensitivity of the insurer's liability to volatility risk.…
Study of estimation errors in surrogate loss minimizers, providing stronger guarantees than existing methods.
problem Estimation errors in surrogate loss minimizers for various hypothesis sets.
method Detailed study of H-consistency estimation error bounds, proving general theorems for distribution-dependent and independent settings. result Explicit bounds for zero-one and adversarial losses, showing enhancements under distributional assumptions.
This paper precisely estimates transformer derivatives for explicit learning guarantees.
problem Computing fully-explicit generalization bounds for transformers with precise higher-order derivative estimates.
method Analyzes and estimates all higher-order derivatives of transformers with multiple attention heads and layer normalization.
result Obtains explicit pathwise generalization bounds for transformers learning from non-i.i.d. samples.
We enhance conformal prediction for risk-averse decisions with action-conditional guarantees.
problem Uncertainty quantification and safety guarantees for machine learning decisions.
method Action-conditional conformal prediction, pinball-loss minimization.
result Action-conditional prediction sets optimize risk-averse decision-making.
New quasi-Newton method guarantees global superlinear convergence.
problem Global convergence and superlinear convergence of quasi-Newton methods.
method Hybrid proximal extragradient method with online learning for Hessian approximation.
result First globally convergent quasi-Newton method with explicit superlinear convergence rate.
We consider the dynamic linear regression problem, where the predictor vector may vary with time. This problem can be modeled as a linear dynamical system, with non-constant observation operator, where the parameters that need to be learned are the variance of both the process noise and the observation noise. While var…
The paper provides convergence guarantees for VAEs using SGD and Adam.
problem Understanding theoretical convergence guarantees for VAEs.
method Derives non-asymptotic convergence rates for VAEs trained with SGD and Adam.
result Convergence rate of \(\mathcal{O}(\log n / \sqrt{n})\) with explicit hyperparameter dependencies.
The paper addresses score-mismatched diffusion models and zero-shot conditional samplers.
problem Theoretical guarantees for score-mismatched diffusion models in zero-shot conditional sampling.
method Theoretical analysis of score-mismatched diffusion models and zero-shot conditional samplers.
result Theoretical performance guarantees with explicit dimensional dependencies for score-mismatched diffusion samplers.
Study on convergence of Langevin dynamics for zero-sum games in probability distributions.
problem Analyzing convergence of Langevin dynamics for zero-sum games in probability distributions.
method Proved exponential and biased convergence guarantees for mean-field and finite-particle min-max Langevin dynamics.
result Explicit iteration complexity for finite-particle algorithms to approximate equilibrium distributions.
Continuous-time PCD for MLE with explicit error bounds.
problem Maximum likelihood estimation of unnormalised densities.
method Continuous-time formulation as coupled SDEs, deriving UiT bounds.
result Explicit error bounds between PCD iterates and MLE solution.
Differential privacy of Gaussian process posterior sampling
problem Privacy of posterior sample paths from Gaussian process
method Intrinsic randomness yields DP guarantees
result Intrinsic randomness yields DP guarantees
This paper presents an asynchronous incremental aggregated gradient algorithm and its implementation in a parameter server framework for solving regularized optimization problems. The algorithm can handle both general convex (possibly non-smooth) regularizers and general convex constraints. When the empirical data loss…
Gradient filters track moving parameters under noisy data and misspecification.
problem Tracking multidimensional time-varying parameters under noisy observations and model misspecification.
method Gradient-based filters update parameters using the gradient of a postulated objective function, evaluated at either the predicted or updated parameters.
result Novel sufficient conditions for exponential stability of the filtered parameter path, and finite-sample and asymptotic mean squared error bounds.
PAC-Bayesian theory applied to learning optimization algorithms with generalization guarantees.
problem Learning optimization algorithms with provable generalization guarantees and explicit trade-offs.
method PAC-Bayes theory applied to learning-to-optimize, reformulating the learning procedure into a one-dimensional minimization problem.
result Learned optimization algorithms outperform deterministic worst-case analysis algorithms, even in the limit case of guaranteed convergence.
The study provides statistical guarantees for Bayesian variational boosting.
problem Statistical and convergence issues in variational boosting.
method Proposed a novel variational family and a functional Frank-Wolfe optimization algorithm.
result Demonstrated stochastic boundedness and provided convergence rate for boosting iterates.
Kernel ridgeless regression with random features shows good generalization without explicit regularization.
problem Generalization of kernel ridgeless regression without explicit regularization.
method Investigation of ridgeless regression with random features and stochastic gradient descent, exploring the effect of random features error and spectral density optimization.
result Random features error exhibits the double-descent curve, leading to improved generalization.
Alternating Direction Method of Multipliers (ADMM) is a widely used tool for machine learning in distributed settings, where a machine learning model is trained over distributed data sources through an interactive process of local computation and message passing. Such an iterative process could cause privacy concerns o…
Statistical guarantees for hyperparameter selection
problem Hyperparameter selection in AI systems
method Learn-then-test framework
result Provable reliability and safety
Develops a unified framework for valuing insurance products with guarantees.
problem Valuing insurance products with guarantees in an affine setting.
method General affine approach to model financial markets, mortality, and policyholder behavior.
result Explicit valuation formulas for variable annuities and related contracts derived.
A new learning method for prosthetic arms without explicit rewards.
problem Learning a prosthetic arm to interact with users without explicit reward signals.
method Interaction-Grounded Learning, observing multidimensional context and feedback vectors, discovering latent reward signal.
result The algorithm can discover a latent reward signal and ground its policies for successful interaction.
Variable annuities (VA) are popular insurance products. VAs provides the insured with a guaranteed accumulation rate on their premium at maturity. In addition, the insured may receive extra benefit if returns of underlying funds are high enough. Here we consider a special case of VA with high-water mark feature and Gua…
The aim of this paper is to solve an optimal investment, consumption and life insurance problem when the investor is restricted to capital guarantee. We consider an incomplete market described by a jump-diffusion model with stochastic volatility. Using the martingale approach, we prove the existence of the optimal stra…
Recent years have seen a flurry of activities in designing provably efficient nonconvex procedures for solving statistical estimation problems. Due to the highly nonconvex nature of the empirical loss, state-of-the-art procedures often require proper regularization (e.g. trimming, regularized cost, projection) in order…
We consider the problem of efficient randomized dimensionality reduction with norm-preservation guarantees. Specifically we prove data-dependent Johnson-Lindenstrauss-type geometry preservation guarantees for Ho's random subspace method: When data satisfy a mild regularity condition -- the extent of which can be estima…
Audited Conformal Prediction improves conditional coverage in pretrained models under distribution shift.
problem Uncertainty quantification for pretrained models under unknown distribution shift
method Leverages a small labeled dataset to train an audit model for marginal coverage, integrates outputs into conformal prediction framework
result Significantly higher conditional coverage than existing approaches
New methods adapt conformal prediction to unknown subpopulation shifts.
problem Failure of conformal prediction under unknown subpopulation shifts.
method Proposes new methods that adapt conformal prediction to unknown subpopulation shifts without explicit subpopulation labels.
result Ensures valid coverage guarantees without explicit knowledge of subpopulation structure.
We design a general framework for answering adaptive statistical queries that focuses on providing explicit confidence intervals along with point estimates. Prior work in this area has either focused on providing tight confidence intervals for specific analyses, or providing general worst-case bounds for point estimate…
The paper develops a valuation framework for GLWB-LTC contracts with Levy dynamics and stochastic interest rates.
problem Valuation of GLWB-LTC contracts with financial guarantees, longevity protection, and health-contingent LTC payments.
method Coupling a recombining Hull-White trinomial tree with an IMEX finite difference scheme, incorporating a seven-state health model.
result Hybrid tree-IMEX method delivers stable long-maturity prices consistent with simulation benchmarks.
This paper extends to dimension 4 the results in the article "Second Order Families of Special Lagrangian 3-folds" by Robert Bryant. We consider the problem of classifying the special Lagrangian 4-folds in C^4 whose fundamental cubic at each point has a nontrivial stabilizer in SO(4). Points on special Lagrangian 4-fol…
Many scientific datasets are of high dimension, and the analysis usually requires visual manipulation by retaining the most important structures of data. Principal curve is a widely used approach for this purpose. However, many existing methods work only for data with structures that are not self-intersected, which is …
MMCGAN uses explicit manifold learning to improve GAN performance.
problem GAN mode collapse and unstable training.
method Introduces Minimum Manifold Coding (MMC) as a prior to guide GAN training.
result MMCGAN effectively alleviates mode collapse and stabilizes GAN training.
Improves probability distribution compression with KT algorithm.
problem Efficiently compressing probability distributions.
method Kernel thinning (KT) algorithm with four improvements.
result KT yields tighter, dimension-free guarantees for any kernel.
We consider the problem of recovering low-rank matrices from random rank-one measurements, which spans numerous applications including covariance sketching, phase retrieval, quantum state tomography, and learning shallow polynomial neural networks, among others. Our approach is to directly estimate the low-rank factor …
BOE reformulates BO as a classifier for scalable batch optimisation.
problem Scalable batch optimisation of expensive functions.
method Reformulates BO as density-ratio estimation, removing need for explicit function prior.
result Theoretical guarantees and improved uncertainty estimates for batch optimisation.
We study the problem of portfolio insurance from the point of view of a fund manager, who guarantees to the investor that the portfolio value at maturity will be above a fixed threshold. If, at maturity, the portfolio value is below the guaranteed level, a third party will refund the investor up to the guarantee. In ex…
New algorithm learns Koopman operator online, with complexity control and convergence guarantees.
problem Online learning of Koopman operator for general nonlinear systems.
method Sparse online learning via stochastic approximation, RKHS action, CME operator.
result Provably convergent algorithm with finite-time guarantees in mis-specified setting.
Motivated by manifold learning techniques, we give an explicit lower bound for how far a smoothly embedded compact submanifold in RN can move in a normal direction and remain an embedding. In addition, given a penalty function P:Emb(M,RN)→R on the space of embeddi…
In this paper we study the pricing and hedging problem of a portfolio of life insurance products under the benchmark approach, where the reference market is modelled as driven by a state variable following a polynomial diffusion on a compact state space. Such a model guarantees not only the positivity of the OIS short …
Model-based reinforcement learning (RL) is considered to be a promising approach to reduce the sample complexity that hinders model-free RL. However, the theoretical understanding of such methods has been rather limited. This paper introduces a novel algorithmic framework for designing and analyzing model-based RL algo…
New risk class penalizes loss deviations from mean on both sides.
problem Current risks are sensitive to loss tails on the upside and ignore the downside.
method Introduces a bi-directional risk class with flexible tail sensitivity.
result Derives high-probability learning guarantees without gradient clipping.
Two new algorithms improve Q* approximation in batch RL with linear error propagation.
problem Improving Q* approximation in batch reinforcement learning.
method Two novel algorithms that estimate Bellman error directly, without quadratic dependence.
result Linear-in-horizon error propagation for batch RL algorithms.
This paper improves a local-to-global principle for Morse quasigeodesics.
problem Quantify the size of local neighborhoods for global Morse behavior.
method Estimates in symmetric space to supplement Kapovich-Leeb-Porti's proof.
result Explicit criteria for local-to-global principle verified.
New approach uses Gaussian processes to learn and track complex systems with guaranteed accuracy.
problem Inaccurate first principle models for complex systems due to data complexity.
method Bayesian prediction error bound for Gaussian process regression, derived from kernel-based data density.
result Achieves vanishing tracking error with increasing data density, providing time-varying accuracy guarantees.
PAC-Bayes bounds for Gibbs posteriors derived via singular learning theory.
problem Generalization bounds for overparameterized models with data-dependent priors.
method Explicit non-asymptotic PAC-Bayes bounds using singular learning theory.
result Explicit posterior-averaged risk bounds for overparameterized models.
Efficient algorithm reduces control system regret to sqrt(t).
problem Control of linear quadratic systems with guaranteed anytime performance.
method Combines SDP-based framework with regularization and perturbation mechanisms.
result Achieves anytime regret of order sqrt(t) with explicit dependence on system dimensions.