Paper proposes robust estimators for heavy-tailed data with infinite variance.
problem Developing robust estimators for heavy-tailed data with infinite variance.
method Proposes two robust estimators: ridge log-truncated M-estimator and elastic net log-truncated M-estimator.
result Demonstrates robustness of log-truncated estimations over standard estimations through simulations and real data analysis.
The paper analyzes and mitigates biases in scalable Gaussian Process methods.
problem Modeling biases in scalable Gaussian Process methods.
method Randomized truncation estimators to eliminate bias in exchange for increased variance.
result Randomized truncation estimators meaningfully outperform biased counterparts with minimal additional computation.
Unified algorithm for Bayesian optimization and level-set estimation.
problem Efficiently optimizing and estimating in settings with pointwise costs and heteroscedastic noise.
method Truncated Variance Reduction (TruVaR) algorithm that greedily shrinks a sum of truncated variances.
result Unified theoretical guarantee for TruVaR covering pointwise costs and heteroscedastic noise.
We study how the presence of correlations in physical variables contributes to the form of probability distributions. We investigate a process with correlations in the variance generated by (i) a Gaussian or (ii) a truncated Lévy distribution. For both (i) and (ii), we find that due to the correlations in the variance,…
Truncated Lévy flights are random walks in which the arbitrarily large steps of a Lévy flight are eliminated. Since this makes the variance finite, the central limit theorem applies, and as time increases the probability distribution of the increments becomes Gaussian. Here, truncated Lévy flights with correlated fluct…
A new method reduces variance in PG methods for RL, improving efficiency and convergence.
problem Improving sample efficiency and convergence of policy gradient methods in reinforcement learning.
method Proposes a gradient truncation mechanism and designs TSIVR-PG method to maximize rewards and utility.
result Shows sample complexity of TSIVR-PG to find ε-stationary policy and global ε-optimal policy.
Paper defines new risk measures for elliptical distributions.
problem Risk measurement for elliptical distributions.
method DTM, DTS, DTK definitions and formula derivation for specific distributions.
result Explicit formulas for DTE, DTV, DTS, and DTK for various distributions.
Proposes a new method to estimate Bayesian neural network depth.
problem Estimating the depth of Bayesian neural networks.
method Uses a discrete truncated normal distribution to learn depth mean and variance, inferring posterior distributions by minimizing variational free energy.
result Improves test accuracy and reduces posterior depth variance on the spiral dataset.
Boundary effects inflate variance in Gaussian processes, leading to acquisition bias.
problem Boundary-induced acquisition bias in Gaussian processes.
method Traced root cause to geometric mechanism of kernel truncation at domain boundaries.
result Boundary effects create distortion that worsens with dimensionality, affecting acquisition behavior.
Paper proposes using truncated normal distribution for RRC model, improving detection of minority classes.
problem Improving weak classifiers in RRC models.
method Proposes using truncated normal distribution and soft confusion matrix for RRC model.
result Truncated-normal-based SCM algorithm outperforms beta distribution in discovering minority classes.
Variance-Calibrated Modulation (VCM) addresses the likelihood trap in LLMs by reshaping the probability distribution before truncation.
problem LLMs fall into the likelihood trap, leading to repetitive degeneration and vocabulary dullness.
method VCM reshapes the probability distribution before truncation through Contextual Searchlight and Adaptive Self-Debiasing.
result VCM mitigates the likelihood trap across open-ended generation, factual QA, and mathematical reasoning.
ES-Single uses ES to estimate gradients in unrolled graphs, reducing variance and improving performance.
problem Estimating gradients in unrolled computation graphs with low variance and stability.
method Evolution strategies (ES) applied to unrolled graphs, with a single perturbation per particle.
result ES-Single reduces variance compared to PES, leading to better performance in various tasks.
The discrete-time mean-variance portfolio selection formulation, a representative of general dynamic mean-risk portfolio selection problems, does not satisfy time consistency in efficiency (TCIE) in general, i.e., a truncated pre-committed efficient policy may become inefficient when considering the corresponding trunc…
Improved SGD for sparse data with faster convergence and better stability.
problem Slow convergence and high variance in sparse online learning for high-dimensional sparse data.
method Stabilized truncated stochastic gradient descent with adaptive shrinkage and annealing strategy.
result Our algorithm achieves better prediction accuracy, sparsity, and stability compared to the original method.
CPCR mitigates bias in PCR for overparameterized models.
problem Bias in Principal Component Regression (PCR) for overparameterized models.
method Calibrated Principal Component Regression (CPCR) learns a low-variance prior in the PC subspace and calibrates the model in the original feature space.
result CPCR outperforms standard PCR in overparameterized settings, improving prediction across multiple problems.
Paper tackles heavy-tailed data without finite variance, proposing robust risk minimization.
problem Empirical risk minimization under heavy-tailed data with finite p p p -th moment. method Minimizes risk values robustly estimated via Catoni's method, using generalized generic chaining.
result Shows better performance of optimizer based on empirical risks via Catoni-style estimation.
The paper estimates common mean of entangled Gaussians with bounded variances.
problem Estimating common mean of entangled Gaussians with bounded variances.
method Iteratively averaging truncated samples.
result Achieves error $O \left(\frac{\sqrt{n\ln n}}{m}
ight)$ with high probability when m = Ω ( n ln n ) m=Ω(\sqrt{n\ln n}) m = Ω ( n ln n ) . k-means derived from Gaussian mixture models with isotropic Gaussians.
problem Clustering with Gaussian mixture models.
method Truncated variational EM approximations applied to Gaussian Mixture Models.
result k-means is a special case of variational EM for Gaussian Mixture Models.
PES method reduces bias in gradient estimation for unrolled graphs.
problem High variance and bias in gradient estimation for unrolled computation graphs.
method Divide graph into unrolls, apply ES update, accumulate correction terms.
result PES provides unbiased, low-variance gradient estimates.
New method estimates volatility for processes with jumps of unbounded variation.
problem Estimating volatility of processes with jumps of unbounded variation.
method Developed a new volatility estimator using debiasing of truncated realized quadratic variation.
result Method outperforms existing alternatives in simulations.
New method for unbiased sampling of doubly-intractable distributions.
problem Hard computation of normalizing constants for complex probability distributions.
method Adapting random series truncation and Markov chain coupling for unbiased estimation of 1/Z.
result Estimators with lower variance and higher positive estimates.
Decoding strategies often exclude human-like tokens, creating a detectable gap in generated text.
problem Decoding strategies exclude contextually appropriate but statistically rare tokens, creating a detectable gap in generated text.
method Analysis of 1.8 million texts across 8 language models, 5 decoding strategies, and 53 hyperparameter configurations.
result 8-18% of human-selected tokens fall outside typical truncation boundaries, indicating a detectable gap.
EM algorithm converges to true mean for truncated mixtures of Gaussians.
problem Analyzing EM algorithm for truncated mixtures of two Gaussians.
method Using dynamical systems, probability, and statistics techniques.
result EM converges almost surely to true mean for various measurable sets S.
Optimizes survey design for private mean estimation with reduced variance.
problem Minimizing variance in private mean estimation with privacy constraints.
method Formulates optimal survey design as an optimization problem, determining optimal subsampling sizes to minimize variance.
result Identifies the first privacy-aware stratified sampling scheme that minimizes variance under different privacy mechanisms.
New methods reduce constraint violations to certainty in stochastic optimization.
problem Finding a point with certain constraint satisfaction and near-stationarity.
method Single-loop variance-reduced stochastic first-order methods with truncated momentum schemes.
result Achieves strong convergence guarantees for ε ε ε -stochastic stationary points with certain constraint satisfaction. The study compares Fourier-based pricing methods, identifying the most efficient and accurate.
problem Comparing CPU effort and pricing biases of Fourier-based implementations.
method Numerical analysis of seven Fourier-based implementations, focusing on truncation and discretization errors.
result The multi-strike version of the COS method is notably faster, and the strike-optimized Carr Madan's formula is both faster and more accurate.
New method estimates volatility for Lévy processes with unbounded jumps efficiently.
problem Efficient estimation of volatility for Lévy processes with unbounded jumps.
method Developed a new estimator based on high-order expansions of truncated moments.
result Method outperforms existing alternatives in estimating volatility.
The pricing of options in exponential Levy models amounts to the computation of expectations of functionals of Levy processes. In many situations, Monte-Carlo methods are used. However, the simulation of a Levy process with infinite Levy measure generally requires either to truncate small jumps or to replace them by a …
A new method optimizes diffusion models with recursive likelihood ratios.
problem Efficiently aligning pre-trained diffusion models for specific applications.
method Recursive Likelihood Ratio (RLR) optimizer for Half-Order (HO) fine-tuning.
result The RLR method achieves unbiased and lower-variance gradients, improving model performance.
SUMO provides unbiased log marginal likelihood estimation for latent variable models.
problem Biased estimates of log marginal likelihood in latent variable models.
method Randomized truncation of infinite series for unbiased estimation.
result Models trained with SUMO give better test-set likelihoods than standard methods.
The paper improves PAC-Bayes bounds for losses with finite moments.
problem Bounding generalization for losses with heavy tails and finite moments.
method Truncation method and PAC-Bayes bounds for unbounded losses with heavy tails and bounded variance.
result Bounds interpolate between slow and fast rates depending on the moment.
Truncated SVD provides a simple yet effective method for approximating high-rank matrices.
problem Estimating high-rank positive semi-definite matrices from partial observations or noisy data.
method Truncated SVD applied to an estimate of the matrix.
result Truncated SVD produces a multiplicative approximation of the original matrix in Frobenius norm.
A new method detects anomalies in multivariate streams without unit dependence.
problem Detect anomalies in multivariate streams without unit dependence.
method Proposes SigMahaKNN combining variance norm and path signature.
result SigMahaKNN detects anomalies better than existing methods.
New algorithm approximates conditional expectations with fast convergence.
problem Approximating conditional expectations in stochastic derivative weights.
method Least-squares Monte Carlo with brute-force SVD truncation.
result Convergence rate is arbitrarily fast polynomial in number of samples.
BigGAN achieves state-of-the-art image synthesis on ImageNet.
problem Generating high-fidelity images from complex datasets like ImageNet.
method Trained a large-scale GAN with orthogonal regularization and a truncation trick.
result Improved Inception Score (IS) of 166.5 and Frechet Inception Distance (FID) of 7.4.
New sampling method for Heston model reduces complexity.
problem Efficient sampling for Heston model's time integrated variance.
method Series expansion, change of measure, Chebyshev polynomial approximations.
result Strong, efficient sampling scheme established for Heston model.
The problem of an arbitrary truncated Levy flight description using the method of cumulant approach has been solved. The set of cumulants of the truncated Levy distribution given the assumption of arbitrary truncation has been found. The influence of truncation shape on the truncated Levy flight properties in the Gauss…
Adaptive Monte Carlo methods are recent variance reduction techniques. In this work, we propose a mathematical setting which greatly relaxes the assumptions needed by for the adaptive importance sampling techniques presented by Vazquez-Abad and Dufresne, Fu and Su, and Arouna. We establish the convergence and asymptoti…
Truncated CauchyNMF robustly learns subspaces from noisy data.
problem Outliers in non-negative matrix factorization (NMF) cause failure.
method Proposes Truncated CauchyNMF loss to handle outliers.
result Theoretical analysis and experimental validation show Truncated CauchyNMF's robustness.
Efficiently estimate Boolean product distribution parameters from truncated samples.
problem Estimating parameters of Boolean product distributions from truncated samples.
method Introducing fatness of truncation set, using membership queries, and adapting Stochastic Gradient Descent.
result Efficiently learn Boolean product distributions from truncated samples with small sample complexity.
In the paper "On Truncated Variation of Brownian Motion with Drift" (Bull. Pol. Acad. Sci. Math. 56 (2008), no.4, 267 - 281) we defined truncated variation of Brownian motion with drift, W t = B t + μ t , t ≥ 0 , W_t = B_t + μt, t\geq 0, W t = B t + μ t , t ≥ 0 , where ( B t ) (B_t) ( B t ) is a standard Brownian motion. Truncated variation differs from regular variation by neglect…
AOPU stabilizes NN training by approximating natural gradient, improving stability and convergence.
problem Stability and interpretability in online NN training for industrial soft sensors.
method AOPU truncates gradient backpropagation, optimizing trackable parameters, and approximating natural gradient.
result AOPU achieves stable convergence and superior performance on chemical process datasets.
Two methods improve simulation of European call options under Heston model.
problem Efficient simulation of European call options under Heston model.
method Two strongly convergent and positivity-preserving methods for Cox-Ingersoll-Ross process under Lamperti transformation: truncated Euler and backward Euler methods.
result Explicit truncated Euler method is computationally effective and robust under high volatility, while implicit backward Euler method provides high accuracy and stability.
Optimal algorithm learns Gaussian under halfspace truncation with minimal samples.
problem Learning a Gaussian distribution truncated to an unknown halfspace.
method Efficient algorithm using n = i l d e O ( d 2 / ε 2 ) n = ilde{O}(d^2/\varepsilon^2) n = i l d e O ( d 2 / ε 2 ) samples and runtime dominated by empirical covariance matrix computation. result Optimal sample and time complexity bounds for learning a Gaussian under halfspace truncation.
New method for constructing truncated vine copulas.
problem High-dimensional parameter space in vine copulas.
method Propose a new score and algorithm for constructing truncated vines.
result New algorithms exploit conditional independences.
The paper explores how control variates can reduce variance in Monte Carlo simulations, especially for Sobolev functions.
problem Efficiency of control variates in reducing variance for Monte Carlo simulations.
method Study of a specific quadrature rule using nonparametric regression-adjusted control variates.
result A specific quadrature rule can improve the Monte Carlo rate and achieve the minimax optimal rate under sufficient smoothness assumptions.
Study minimax regret in bilateral trade with heavy-tailed valuations.
problem Minimizing regret in bilateral trade with infinite variance valuations.
method Extended self-bounding property, truncated-mean estimation, epoch-based algorithm.
result Achieves regret bound of O ( T 1 − 2 β ( p − 1 ) / ( β p + d ( p − 1 ) ) ) O(T^{1-2β(p-1)/(βp + d(p-1))}) O ( T 1 − 2 β ( p − 1 ) / ( β p + d ( p − 1 )) ) under specific conditions. Bayesian CRM improves offline learning from logged bandit data.
problem Offline learning from logged bandit feedback.
method PAC-Bayesian analysis for a new generalization bound, novel regularization technique.
result New technique outperforms standard L 2 L_2 L 2 regularization and is competitive with variance regularization.