In this paper, we give a new sharp generalization bound of lp-MKL which is a generalized framework of multiple kernel learning (MKL) and imposes lp-mixed-norm regularization instead of l1-mixed-norm regularization. We utilize localization techniques to obtain the sharp learning rate. The bound is characterized by the d…
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48 results for “mixing rate”
The literature on statistical learning for time series assumes the asymptotic independence or ``mixing' of the data-generating process. These mixing assumptions are never tested, nor are there methods for estimating mixing rates from data. We give an estimator for the -mixing rate based on a single stationary sample…
Paper analyzes distributed learning with non-i.i.d. samples.
problem Learning rate analysis for distributed kernel ridge regression with dependent samples.
method Integral operator approach and covariance inequality for strong mixing sequences.
result Derives optimal learning rates for distributed kernel ridge regression.
The paper analyzes learning schemes for various stationary stochastic processes.
problem Analyzing learning schemes with different stationary stochastic processes.
method Unified treatment of various mixing processes using generalized Bernstein-type inequality.
result Sharp oracle inequalities and convergence rates for learning schemes.
Mixed likelihood GPs improve model performance in human-in-the-loop experiments.
problem Lack of auxiliary information in traditional GPs for human responses.
method Propose mixed likelihood variational GPs to leverage auxiliary information.
result Modeling performance improvements across diverse applications.
Study online learning in RKHS with dependent processes, focusing on \(β\)- and \(φ\)-mixing.
problem Online learning in RKHS with dependent data.
method Online regularized learning algorithm in RKHS, analyzing \(β\)- and \(φ\)-mixing sequences.
result Probabilistic upper bounds and convergence rates for mixing coefficients.
This work improves mixing rates for Bayesian CART, a key component of BART.
problem Understanding and improving mixing rates for Bayesian inference with MCMC.
method Derived upper bounds on mixing times, provided sufficient conditions for polynomial mixing, and proposed Twiggy Bayesian CART.
result Twiggy Bayesian CART achieves polynomial mixing without assuming signal connectivity.
iPMCMC uses interacting samplers for improved mixing rates.
problem Improving mixing rates in Markov chain Monte Carlo methods.
method iPMCMC uses an interacting pool of samplers.
result Significant improvements in mixing rates compared to non-interacting methods.
Paper analyzes Nyström regularization for time series forecasting with sequential sub-sampling.
problem Learning rate analysis of Nyström regularization for -mixing time series.
method Banach-valued Bernstein inequality and integral operator approach for -mixing sequences.
result Almost optimal learning rates for Nyström regularization with sequential sub-sampling.
New algorithm finds mixed Nash equilibria in GANs.
problem No provably convergent algorithm exists for general GANs.
method Developed a novel algorithmic framework via an infinite-dimensional two-player game.
result Proved rigorous convergence rates to the mixed Nash Equilibrium.
Sharp rates found for learning with dependent data, avoiding sample size deflation.
problem Learning with dependent data and square loss.
method Combining weak sub-Gaussian class and mixed tail generic chaining.
result Achieves a rate that only depends on class complexity and second order statistics.
Elo ratings learn model parameters quickly using Markov chains.
problem Ranking players in online settings.
method Bradley--Terry--Luce model and Markov chain theory.
result Elo learns model parameters at a competitive rate.
Approximation and learning of anisotropic and mixed smooth functions by deep ReLU neural networksstat.ML
Deep ReLU networks can approximate and learn smooth functions efficiently.
problem Efficiently approximating and learning smooth functions using deep ReLU neural networks.
method Extending recent results to anisotropic and mixed smooth function classes, establishing approximation rates.
result Deep ReLU networks achieve minimax optimal rates up to logarithmic factors for various smooth function classes.
In this paper we address the following question: Can we approximately sample from a Bayesian posterior distribution if we are only allowed to touch a small mini-batch of data-items for every sample we generate?. An algorithm based on the Langevin equation with stochastic gradients (SGLD) was previously proposed to solv…
Optimizes pension mix of PAYGO, EET, and individual savings.
problem Balancing PAYGO, EET, and individual savings in funded pension schemes.
method Solves a Nash equilibrium between pension participants and government, considering age-dependent preferences and optimal asset allocation.
result Identifies critical ages and optimal contribution rates for maximizing overall utility.
TD(0) with Polyak-Ruppert averaging achieves robust and fast convergence rates
problem TD(0) learning under Markovian sampling
method Polyak-Ruppert averaging with a single stepsize
result Simultaneous high-probability convergence guarantees for TD(0) iterates and PR average
The paper tackles high-dimensional mixed linear regression with unknown parameters and proposes methods for estimation, confidence intervals, and hypothesis testing.
problem High-dimensional mixed linear regression with unknown parameters and covariance structure.
method Iterative high-dimensional EM algorithm for estimating regression vectors, debiased estimators for individual coordinates, and large-scale multiple testing procedure.
result Asymptotic normality of debiased estimators and FDR control for hypothesis testing.
Improves decentralized learning by optimizing graph mixing for data heterogeneity.
problem Data heterogeneity impacts convergence in decentralized learning, but existing methods ignore this.
method Characterized and quantified the relationship between graph mixing and data heterogeneity. Proposed an optimization approach to improve convergence.
result Our approach leads to improved test performance across various tasks.
AM converges super-linearly for solving mixed linear regression problems.
problem Learning linear regressors from unlabeled observations in multiple linear regression models.
method Alternating Minimization (AM) algorithm, which alternates between label estimation and regression solving.
result AM converges super-linearly in certain parameter regimes, requiring only O(log log(1/ε)) iterations to achieve an error of ε.
Mixed-SCORE+ improves community detection in weak signal networks.
problem Detecting communities in weak signal networks.
method Proposes Mixed-SCORE+ combining properties of Mixed-SCORE and SCORE+.
result Significantly improves detection error rates on Polblogs and weak signal networks.
New RL method MAC improves performance in sparse reward settings.
problem Slow mixing in large state spaces or sparse rewards.
method Multi-level Monte Carlo Actor-Critic (MAC) algorithm.
result Achieves convergence rate comparable to state-of-the-art AC algorithms.
Beyond the Independence Assumption: Finite-Sample Guarantees for Deep Q-Learning under -Mixingstat.ML
Study shows DQN's performance degrades with temporal dependence in data.
problem Temporal dependence in replayed data affects DQN's performance.
method Modelled -mixing data, derived risk bounds, and empirical validation.
result Temporal dependence leads to a degradation in DQN's performance rate.
Temporal Difference Learning analysis under non-i.i.d. data and nonlinear approximation.
problem Finite-sample behavior of TD(0) under non-i.i.d. data and nonlinear approximation.
method High-probability, finite-sample analysis of vanilla TD(0) on polynomially mixing Markov data, assuming Holder continuity and bounded generalized gradients.
result Bounds on the convergence rate of TD(0) with high probability, matching known i.i.d. rates and holding even with nonstationary initialization.
Nearly Maximally Predictive Features and Their Dimensionscond-mat.stat-mech
New bounds on nearly maximally predictive features help improve data prediction.
problem Inferring maximally predictive features from data sets is often uncountably infinite.
method Derived upper-bounds on the number and coding cost of nearly maximally predictive features.
result Mixed-state predictive features offer a substantial improvement over finite-order Markov models.
Study fast learning rates for square loss in dependent data with hypercontractivity condition.
problem Learning from dependent data with fast rates matching independent data.
method Martingale difference noise, trajectory hypercontractivity condition, least-squares estimator.
result Excess risk bound matches iid rate after burn-in time, independent of mixing-time.
The study proves exponential mixing for specific Weil-Petersson flows in exceptional moduli spaces.
problem Analyzing mixing rates of geodesic flows in moduli spaces with cusps.
method New method of analyzing invariant foliations for hyperbolic flows with singularities, using metric changes and flow rescaling.
result Exponential mixing for Weil-Petersson flows in and , contrasting with non-exponential mixing in other moduli spaces.
Estimates mixing coefficients of geometrically ergodic Markov processes from a single sample path.
problem Estimating mixing coefficients of geometrically ergodic Markov processes.
method Proposes methods to estimate -mixing coefficients from a single sample path under standard smoothness conditions.
result Obtains a rate of convergence of order \(\mathcal{O}(\log(n) n^{-[s]/(2[s]+2)})\) for the expected error of the estimator.
New method adapts to unknown mixing time in stochastic optimization.
problem Optimizing with Markovian data where mixing time is unknown.
method Combines MLMC gradient estimation with adaptive learning.
result Achieves optimal convergence rate for convex problems.
Paper proposes deep neural networks for nonparametric regression from dependent data.
problem Nonparametric regression from strongly mixing observations.
method Minimum error entropy principle applied to deep neural networks.
result Deep neural networks achieve minimax optimal convergence rates for Gaussian errors.
Enhances stochastic gradient methods with accelerated dynamics.
problem Reducing computational cost in large dataset learning.
method Proposes a novel technique using accelerated stochastic dynamics to mitigate stochasticity in the stochastic Langevin gradient method.
result Demonstrates improved convergence and reduced correlation time through violating the detailed balance condition.
Develops a bi-variate stochastic framework to model mortality and interest rates with long-range dependence.
problem Captures long-range dependence and instantaneous correlation in mortality and interest rates.
method Mixed fractional Brownian motions, analytical solutions, risk-neutral measure, sequential parameter estimation.
result Explicit pricing of zero-coupon bonds and extreme mortality bonds, practical implications for pricing and risk management.
Study nonstationary data learning under β-mixing processes.
problem Learning from nonstationary data with varying distributions.
method Proposed a learning method for β-mixing processes.
result Cumulative excess risk grows sublinearly in the number of predictions.
Mixed dimension embeddings reduce memory usage in recommendation systems.
problem Space-intensive embedding representations in recommendation systems.
method Mixed dimension embeddings where vector dimension scales with query frequency.
result Significant reduction in memory usage with minimal performance loss.
On the Minimax Optimality of the EM Algorithm for Learning Two-Component Mixed Linear Regressionstat.ML
EM algorithm achieves optimal sample complexity for learning two-component mixed linear regression.
problem Learning two-component mixed linear regression under varying signal-to-noise ratios.
method Analysis of EM algorithm convergence rates under different SNR regimes.
result EM algorithm achieves minimax optimal sample complexity in all SNR regimes.
Estimates geodesic count on hyperbolic surfaces.
problem Counting simple closed geodesics on hyperbolic surfaces.
method Exponential mixing rate for Teichmüller geodesic flow.
result Proves a quantitative estimate for geodesic length.
Develops a contraction framework for MCMC mixing rates.
problem Proving mixing-time bounds for MCMC algorithms.
method Global and local contraction coefficients under -divergence.
result Explicit global contraction coefficients for Gaussian smoothing.
Paper develops a novel approach for classifying high-dimensional mixed data.
problem Handling datasets with both categorical and continuous variables of high dimensions.
method Location model with Gaussian conditional distributions, kernel smoothing for bandwidth choice, penalized likelihood estimation.
result Competitive performance of the proposed classifier demonstrated through simulations and real data.
Accelerates sampling from Gibbs distributions using ARWP method.
problem Sampling from Gibbs distributions efficiently.
method ARWP method, combining Nesterov acceleration and regularized Wasserstein proximal.
result ARWP exhibits higher contraction rate and faster tail exploration.
BC learning improves image classification by mixing images from different classes.
problem Improving image classification accuracy.
method Generates mixed images from different classes and trains models to output the mixing ratio.
result Significant improvement in image classification performance (19.4% and 2.26% top-1 errors on ImageNet-1K and CIFAR-10, respectively).
New adaptive NMF methods improve recommendation accuracy.
problem Improving recommendation accuracy in recommender systems.
method Adaptive Nonnegative Matrix Factorization (NMF) with mixed strategies.
result New algorithms outperform classical methods in reconstruction of missing ratings.
About the Justification of Experience Rating: Bonus Malus System and a new Poisson Mixture Modelq-fin.RM
The claim experience of the past is a very important information to calculate the fair price of an insurance contract. In a lot of European countries for instance the prices for motor car insurance depend on the number of claims the driver has reported to the insurance company during the last years. Classically these p…
This paper studies convergence behavior of latent mixing measures that arise in finite and infinite mixture models, using transportation distances (i.e., Wasserstein metrics). The relationship between Wasserstein distances on the space of mixing measures and f-divergence functionals such as Hellinger and Kullback-Leibl…
Estimates mixing time of non-reversible Markov chains from a single trajectory.
problem Estimating mixing time of non-reversible Markov chains from a single trajectory.
method Estimates pseudo-spectral gap instead of spectral gap, achieving polynomial dependence on minimal stationary probability and pseudo-spectral gap.
result Achieves polynomial dependence on minimal stationary probability and pseudo-spectral gap, overcoming the loss of symmetry.
Ballistic Convergence in Hit-and-Run Monte Carlo and a Coordinate-free Randomized Kaczmarz Algorithmmath.PR
Paper analyzes Hit-and-Run's convergence rates and applies similar methods to randomized Kaczmarz.
problem Quantifying advantages of Hit-and-Run's coordinate-free property.
method Sharp estimates via coupling methods and mixing time bounds.
result Ballistic and superdiffusive convergence rates in certain settings.
Estimates Markov chain mixing time from a single trajectory.
problem Estimating mixing time of Markov chains from a single trajectory.
method Contraction with respect to total variation, inspired by Wolfer's contraction coefficient.
result Improved confidence intervals and instance-dependent rates for estimating Markov chains.
DiMMSB models directed mixed membership networks, identifying distinct community structures.
problem Modeling directed mixed membership networks with distinct community structures.
method Directed Mixed Membership Stochastic Blockmodel (DiMMSB) with DiSP algorithm.
result DiSP algorithm is asymptotically consistent and outperforms competitors.
The paper tackles long-context linear system identification with improved sample complexity bounds.
problem Identifying dynamical systems with long dependencies over fixed context windows.
method Established sample complexity bounds for systems with linear dependencies over a context window of length p.
result The learning process is not hindered by slow mixing properties in extended context windows.
New framework relaxes independence assumption for graph-mixing dependencies.
problem Tackles limitations of existing generalization results for graph-mixing dependencies.
method Proposes a framework where dependencies decay with graph distance, derives generalization bounds leveraging online-to-PAC framework.
result Derives high-probability generalization guarantees that depend on mixing rate and graph's chromatic number.