New unbiased gradient estimators for complex optimization problems.
problem Unbiased and variance-limited gradient estimation for conditional stochastic optimization.
method Developed multilevel Monte Carlo gradient estimators for conditional stochastic optimization problems.
result Unbiased and finite variance gradient estimators for conditional stochastic optimization problems.
New estimator for symmetric kernel expectations, robust to missing data.
problem Efficient estimation of symmetric kernel expectations with missing data.
method Median-of-Incomplete-U-Statistics (MIU) estimator.
result Established finite-sample concentration rate for MIU.
Paper proposes a new estimator for nested expectations with faster convergence.
problem Estimating nested expectations is computationally challenging.
method Nested kernel quadrature estimators with proof of faster convergence rate.
result The proposed method requires fewer samples for accurate estimation.
New method optimizes risk estimation for financial losses.
problem Estimating expected shortfall risk for heavy-tailed distributions.
method Proposes a novel estimator for expected shortfall robust to data corruption.
result Demonstrates superior performance and robustness compared to classical methods.
The problem of estimation error of Expected Shortfall is analyzed, with a view of its introduction as a global regulatory risk measure.
FKEE estimates expectations without samples, using diffusion bridges and PINNs.
problem Estimating expectations without large sample sizes.
method Diffusion bridge models and Feynman-Kac operator approximation using PINNs.
result Significantly reduces variance and improves efficiency.
GBC methods compute expected utility without needing the model's density.
problem Computing expected utility in complex models.
method Density-free generative method using quantile neural estimator.
result Efficient estimation of expected utility from simulated data.
Proposes data-driven methods for estimating conditional expectations.
problem Estimating conditional expectations when underlying density is unknown.
method Data-driven techniques to directly estimate conditional expectations from training data.
result Extends data-driven method to solve nonlinear equations in stochastic optimization.
Paper tackles conditional expectation estimation using compactification operators.
problem Estimating conditional expectations from product of two random variables.
method Operator theoretic approach using kernel integral operators in reproducing kernel Hilbert space.
result Solutions allow numerical approximation and convergence of data-driven implementations.
Estimates MLP expected output without sampling, using fewer FLOPs.
problem Estimating expected loss in machine learning efficiently.
method Approximate representations of activations using cumulants and Hermite expansions.
result Estimates expected output with fewer FLOPs than Monte Carlo sampling.
Optimal transport framework for density estimation with constraints.
problem Density estimation under expectation constraints.
method Minimizes Wasserstein distance subject to expected value constraints and regularization.
result Framework effectively addresses non-smooth constraints through annealing-like algorithm.
CAESar improves risk forecasting by combining VaR and ES estimates.
problem Lack of tail risk measures in financial risk management.
method Conditional Autoregressive Expected Shortfall model, combining VaR and ES estimates.
result CAESar outperforms existing methods in risk forecasting.
Quantum algorithm speeds up nested expectation estimation by nearly quadratically.
problem Estimating repeatedly nested expectations with quantum computing.
method Proposes a quantum algorithm achieving nearly quadratic speedup over classical methods.
result Achieves nearly quadratic speedup for RNEs, up to logarithmic factors.
A new method estimates expectations from subtractive mixture models without sampling.
problem Estimating expectations from multimodal distributions using SMMs.
method Difference representation of SMMs to create unbiased IS estimator (ΔextEx). result Demonstrates that ΔextEx can achieve comparable estimation quality to auto-regressive sampling but is faster. Extended univariate Range Value-at-Risk to multivariate settings.
problem Inability of traditional risk measures for heavy-tail distributions and infinite tail expectations.
method Multivariate definitions of robust truncated tail expectations, robustness and properties derived, closed-form expressions and special cases discussed.
result Empirical estimators accuracy examined through numerical and graphical examples.
In stochastic decision problems, one often wants to estimate the underlying probability measure statistically, and then to use this estimate as a basis for decisions. We shall consider how the uncertainty in this estimation can be explicitly and consistently incorporated in the valuation of decisions, using the theory …
Estimates expected information gain using density approximations and dimension reduction.
problem Estimating expected information gain in nonlinear and non-Gaussian settings.
method Flexible transport-based schemes for EIG estimation, optimal sample allocation, and gradient-based upper bounds on mutual information.
result Optimal sample allocation and dimension reduction schemes improve EIG estimation accuracy and convergence rate.
The contour map of estimation error of Expected Shortfall (ES) is constructed. It allows one to quantitatively determine the sample size (the length of the time series) required by the optimization under ES of large institutional portfolios for a given size of the portfolio, at a given confidence level and a given esti…
Expected signatures map data streams to lower dimensions, improving ML performance.
problem Leveraging model-free embeddings for domain-agnostic machine learning.
method Expected signatures map data streams to lower dimensions, with convergence results bridging empirical and theoretical estimators.
result A modified expected signature estimator with lower mean squared error for martingale processes.
New estimator reduces nested expectation estimation costs.
problem Estimating repeatedly nested expectations is computationally expensive.
method Recursive Estimator for Arbitrary Depth (READ) using randomized multilevel Monte Carlo.
result Optimal computational cost of O(ε^(-2)) for every fixed D.
Paper proposes an unbiased optimization method for Bayesian experimental design.
problem Maximizing expected information gain in Bayesian experimental design.
method Randomized multilevel Monte Carlo (MLMC) method combined with stochastic gradient descent.
result An unbiased estimator for the gradient of expected information gain.
Expected Shortfall (ES) in several variants has been proposed as remedy for the defi-ciencies of Value-at-Risk (VaR) which in general is not a coherent risk measure. In fact, most definitions of ES lead to the same results when applied to continuous loss distributions. Differences may appear when the underlying loss di…
A new EM algorithm improves inference from large datasets.
problem Efficient inference in latent variable models with large datasets.
method Introduces SPIDER-EM, a novel EM algorithm using SPIDER estimator.
result Finite-time complexity bounds for smooth non-convex likelihood.
Develops methods to estimate ratios of conditional expectation functions.
problem Estimating ratios of conditional expectation functions in causal inference.
method Orthogonal series estimator combined with debiased machine learning techniques.
result Valid pointwise and uniform asymptotic results for estimation and inference on CEFR.
Many problems in machine learning and statistics involve nested expectations and thus do not permit conventional Monte Carlo (MC) estimation. For such problems, one must nest estimators, such that terms in an outer estimator themselves involve calculation of a separate, nested, estimation. We investigate the statistica…
New method improves robustness of Bayesian experimental design.
problem Bayesian experimental design's sensitivity to prior distribution changes.
method Introduces robust expected information gain (REIG) and uses KL-divergence ambiguity sets.
result REIG stabilizes sampling-based EIG estimation and compensates for prior variability.
Novel approach for estimating conditional expectations using Bayesian quadrature.
problem Estimating conditional expectations with costly evaluations.
method Probabilistic numerical methods incorporating prior smoothness knowledge.
result Fast convergence rate and uncertainty quantification.
A non-Euclidean generalization of conditional expectation is introduced and characterized as the minimizer of expected intrinsic squared-distance from a manifold-valued target. The computational tractable formulation expresses the non-convex optimization problem as transformations of Euclidean conditional expectation. …
Adapts EGOP to multi-class setting and proposes a simple rough estimator.
problem Recovering relevant directions for multi-class regression.
method Adapt EGOP to multi-class setting, propose a simple rough estimator.
result Simple rough estimator of EJOP remains statistically consistent.
Estimation of tail quantities, such as expected shortfall or Value at Risk, is a difficult problem. We show how the theory of nonlinear expectations, in particular the Data-robust expectation introduced in [5], can assist in the quantification of statistical uncertainty for these problems. However, when we are in a hea…
New EP variants improve inference stability and efficiency.
problem Inference stability and efficiency issues in EP.
method Motivated by natural-gradient optimization, new EP variants are introduced that are robust to Monte Carlo noise and efficient with single samples.
result Improved stability and efficiency in inference tasks.
To address the challenge of backpropagating the gradient through categorical variables, we propose the augment-REINFORCE-swap-merge (ARSM) gradient estimator that is unbiased and has low variance. ARSM first uses variable augmentation, REINFORCE, and Rao-Blackwellization to re-express the gradient as an expectation und…
A new unbiased Hessian estimator for expectation-based objectives.
problem Estimating Hessian for objectives with non-reparameterizable nodes.
method GO Hessian estimator for expectation-based objectives.
result GO Hessian provides unbiased and low-variance estimation of Hessian.
Bayesian method for estimating quantile sets efficiently.
problem Estimating quantile sets of expensive-to-evaluate functions.
method Bayesian active learning with Gaussian process modeling and Expected Estimator Modification (EEM).
result Efficient estimation of small quantile sets.
Study shows the corrected Akaike criterion is inadmissible for estimating Kullback-Leibler discrepancy.
problem Inadmissibility of the corrected Akaike information criterion for estimating Kullback-Leibler discrepancy.
method Loss estimation framework to demonstrate inadmissibility and provide improved estimators.
result Improved estimators of Kullback-Leibler discrepancy are provided and perform well in reduced-rank situations.
Develops methods to estimate gradient of EIG for Bayesian Experimental Design.
problem Optimizing Bayesian inference through efficient experimental design.
method Introduces UEEG-MCMC and BEEG-AP methods for estimating EIG gradient.
result Both methods improve upon existing benchmarks in EIG optimization.
New method for unbiased regression reduces excess risk.
problem Least squares regression with optimal solution and Hessian matrix.
method Averaged stochastic gradient descent with time-average estimator.
result Unbiased estimator with O(1/k) expected excess risk.
Paper improves VaR risk allocation by avoiding zero probability events.
problem Computing VaR contributions for zero probability events.
method Reformulates Euler contributions to a ratio of conditional expectations with strictly positive probability events.
result Proposed estimator outperforms standard Monte Carlo methods in bias and variance.
Paper measures cognitive bias in positive feedback trading using diffusion process estimates.
problem Measuring cognitive bias in positive feedback trading behavior.
method Conditional estimates of diffusion processes to quantify bias, proving asymptotic properties.
result Bias in positive feedback trading converges to zero over time, leading to adaptive expectations.
Most conventional Reinforcement Learning (RL) algorithms aim to optimize decision-making rules in terms of the expected returns. However, especially for risk management purposes, other risk-sensitive criteria such as the value-at-risk or the expected shortfall are sometimes preferred in real applications. Here, we desc…
Improved nonparametric regression with debiasing for root-n consistency.
problem Challenges in achieving root-n consistency and normal distribution for nonparametric estimators.
method Debiasing technique by adding a correction term to nonparametric estimators.
result Achieves root-n consistency and asymptotic normality.
Approximations of loopy belief propagation, including expectation propagation and approximate message passing, have attracted considerable attention for probabilistic inference problems. This paper proposes and analyzes a generalization of Opper and Winther's expectation consistent (EC) approximate inference method. Th…
In this paper we formulate the nonnegative matrix factorisation (NMF) problem as a maximum likelihood estimation problem for hidden Markov models and propose online expectation-maximisation (EM) algorithms to estimate the NMF and the other unknown static parameters. We also propose a sequential Monte Carlo approximatio…
Deep learning improves causal effect estimation from complex observational data.
problem Estimating causal effects from complex observational data with low bias.
method Unified deep learning framework using multitask recurrent neural networks.
result Deep learning estimator shows lower bias in causal effect estimates.
Many problems in financial engineering involve the estimation of unknown conditional expectations across a time interval. Often Least Squares Monte Carlo techniques are used for the estimation. One method that can be combined with Least Squares Monte Carlo is the "Regress-Later" method. Unlike conventional methods wher…
Large graphs abound in machine learning, data mining, and several related areas. A useful step towards analyzing such graphs is that of obtaining certain summary statistics - e.g., or the expected length of a shortest path between two nodes, or the expected weight of a minimum spanning tree of the graph, etc. These sta…
Gradient boosting estimates Riesz representer for causal inference.
problem Estimating causal quantities using traditional methods is challenging and prone to variance issues.
method Gradient boosting algorithm to directly estimate Riesz representer.
result Gradient boosting performs similarly or better than traditional methods in estimating causal quantities.
Paper proposes a probabilistic method to handle missing data in decision trees.
problem Handling missing data in decision trees.
method At deployment time, use density estimators to compute expected predictions. At learning time, fine-tune tree parameters to minimize expected prediction loss.
result Effective compared to baselines in experiments.