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.
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…
Paper introduces a new project control method using Monte Carlo and statistical learning.
problem Project control under uncertainty.
method Integrates Earned Value Methodology with Monte Carlo simulation and statistical learning.
result Estimates probabilities of project success and duration.
This paper develops a Bayesian optimal design of experiments for estimating the statistical expectation of a black-box function.
problem Estimating the statistical expectation of a black-box function in complex systems.
method Sequentially querying the black-box function at specific designs selected by an infill-sampling criterion, maximizing expected information gain.
result Derivation of a semi-analytic mathematical formula for expected information gain about the statistical expectation of a physical response.
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 …
High dimensional structured data such as text and images is often poorly understood and misrepresented in statistical modeling. The standard histogram representation suffers from high variance and performs poorly in general. We explore novel connections between statistical translation, heat kernels on manifolds and gra…
We compute the expected value of the Kullback-Leibler divergence to various fundamental statistical models with respect to canonical priors on the probability simplex. We obtain closed formulas for the expected model approximation errors, depending on the dimension of the models and the cardinalities of their sample sp…
Extends conformal prediction for controlling expected risk of monotone loss functions.
problem Controlling expected risk of monotone loss functions.
method Generalizes split conformal prediction with coverage guarantee, extending to distribution shift, quantile risk, multiple, adversarial, and expectations of U-statistics.
result Tight up to an O(1/n) factor, with worked examples in computer vision and natural language processing. EDAs are shown to be a type of EM algorithm.
problem Understanding and improving Estimation of Distribution Algorithms.
method Connecting EDAs to Expectation-Maximization (EM) framework.
result EDAs can be understood as a special case of EM.
New DP EM algorithm with statistical guarantees for mixture models.
problem Preserving privacy in EM algorithms for mixture models.
method Proposed a DP EM algorithm with statistical guarantees.
result Near optimal estimation error for GMM in DP model.
Model uses statistical physics principles to predict financial market volatility and returns.
problem Predicting price volatility and expected returns in financial markets.
method Inspired by statistical physics, the study introduces a physical model using Level 3 order book data to measure kinetic energy and momentum.
result The model outperforms traditional and machine learning approaches in forecasting volatility and expected returns.
The paper calculates expected distances on partially oriented flag manifolds.
problem Understanding distances on partially oriented flag manifolds.
method Computing expected distances on low-dimensional examples.
result Computed expected distances on partially oriented flag manifolds.
This paper enhances privacy in statistical model checking of cyber-physical systems.
problem Privacy concerns in consumer-level applications due to statistical model checking.
method Proposes expected differential privacy and a new exponential mechanism for sequential algorithms.
result Demonstrates a novel mechanism to preserve privacy in statistical model checking.
Simplified Variational Bayes for easier inference.
problem Complex derivation of Variational Bayes.
method 3-step recipe to identify posterior form and directly write updates.
result Easier, faster, shorter derivation of Variational Bayes.
Paper examines the relationship between maximizing and minimizing expected return in portfolio optimization.
problem Investment risk and return optimization in portfolio problems.
method Lagrange undetermined multiplier method and replica analysis.
result Derived mean square error and correlation coefficient of optimal portfolios as functions of risk tolerance.
Bayesian EP solves CS problems more accurately than other methods.
problem Finding sparse solutions to underdetermined linear systems with constraints.
method Bayesian inference with Expectation Propagation (EP) for marginal distribution computation.
result EP outperforms other methods in solving CS problems with correlated sensing matrices.
We propose a new backtesting framework for Expected Shortfall that could be used by the regulator. Instead of looking at the estimated capital reserve and the realised cash-flow separately, one could bind them into the secured position, for which risk measurement is much easier. Using this simple concept combined with …
We develop a new statistical test for comparing variables with varying scales.
problem Comparing variables with different scales in multidimensional spaces.
method Order based on expectations of random variables, generalized stochastic dominance (GSD) order, regularized statistical test, linear optimization, imprecise probability models.
result Validated through multidimensional data from various fields.
Study excess risk in statistical inference with transformations.
problem Excess risk in estimating random variables from feature vectors and transformations.
method Characterize lossless transformations, develop test statistics, and information-theoretic bounds.
result Strongly consistent partitioning test statistic for lossless transformations.
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.
We provide sharp empirical estimates of expectation, variance and normal approximation for a class of statistics whose variation in any argument does not change too much when another argument is modified. Examples of such weak interactions are furnished by U- and V-statistics, Lipschitz L-statistics and various error f…
This paper attempts to provide a decision-theoretic foundation for the measurement of economic tail risk, which is not only closely related to utility theory but also relevant to statistical model uncertainty. The main result is that the only risk measures that satisfy a set of economic axioms for the Choquet expected …
We provide a general theory of the expectation-maximization (EM) algorithm for inferring high dimensional latent variable models. In particular, we make two contributions: (i) For parameter estimation, we propose a novel high dimensional EM algorithm which naturally incorporates sparsity structure into parameter estima…
A review of statistical SSL methods showing improved classifier performance.
problem Forming classifiers from limited labeled data and many unlabeled data.
method Statistical approaches to semi-supervised learning.
result A classifier from partially labeled data can have lower expected error rate.
This paper bridges statistical and machine learning approaches to variational inference.
problem Statisticians struggle to understand variational inference from a Frequentist perspective.
method Explains VI, VAEs, and DDMs from a Frequentist viewpoint, starting with EM.
result VI emerges as a scalable solution for intractable E-steps in VAEs and DDMs.
This paper presents a new approach, called perturb-max, for high-dimensional statistical inference that is based on applying random perturbations followed by optimization. This framework injects randomness to maximum a-posteriori (MAP) predictors by randomly perturbing the potential function for the input. A classic re…
The paper revisits expected signatures in semimartingale models, providing new formulae and simplifying complexity.
problem Computing expected signatures in semimartingale models.
method Revisits and provides new formulae for computing expected signatures in a general semimartingale setting.
result Log-transform of expected signatures simplifies complexity, leading to signature cumulants.
SMC methods approximate intractable Bayesian inference.
problem Approximating intractable Bayesian inference.
method Sequential Monte Carlo (SMC) methods.
result SMC can approximate intractable expectations and normalizing constants.
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…
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…
The paper analyzes the expected size of conformal prediction sets.
problem Lack of finite-sample analysis and guarantees for prediction set sizes.
method Theoretical quantification and empirical computation of expected set size.
result Derives point estimates and high-probability interval bounds for prediction set size.
We discuss the coherence properties of Expected Shortfall (ES) as a financial risk measure. This statistic arises in a natural way from the estimation of the "average of the 100p % worst losses" in a sample of returns to a portfolio. Here p is some fixed confidence level. We also compare several alternative representat…
Expectation Maximization (EM) is among the most popular algorithms for estimating parameters of statistical models. However, EM, which is an iterative algorithm based on the maximum likelihood principle, is generally only guaranteed to find stationary points of the likelihood objective, and these points may be far from…
A new method for backtesting ES forecasts in banking.
problem Designing a model-free backtesting procedure for Expected Shortfall forecasts.
method Use e-values and e-processes to introduce backtest e-statistics for VaR and ES.
result The proposed method can be applied to various risk measures and statistical quantities.
For a finite function class we describe the large sample limit of the sequential Rademacher complexity in terms of the viscosity solution of a G-heat equation. In the language of Peng's sublinear expectation theory, the same quantity equals to the expected value of the largest order statistics of a multidimensional $…
We analyze a controlled price formation experiment in the laboratory that shows evidence for bubbles. We calibrate two models that demonstrate with high statistical significance that these laboratory bubbles have a tendency to grow faster than exponential due to positive feedback. We show that the positive feedback ope…
Bayesian calibration for BCP self-assembly models using image data and measure transport.
problem Calibrating models of BCP self-assembly from image data with aleatory uncertainty.
method Likelihood-free inference via measure transport and summary statistics.
result Expected information gains can be computed efficiently for model calibration.
Paper compares hard and soft EM for BN learning from incomplete data.
problem Learning BNs from incomplete data using EM algorithms.
method Investigates the impact of imputation vs. belief propagation in hard and soft EM.
result A decision tree can guide practitioners in choosing the best EM algorithm.
A new gradient method reduces variance for non-reparameterizable distributions.
problem Efficient calculation of unbiased gradients for expectation-based objectives.
method GO Gradient, which applies to non-reparameterizable distributions and has low variance.
result GO Gradient reduces variance to the same level as reparameterization trick with one sample.
Estimates and quantizes expected persistence diagrams for efficient analysis.
problem Statistical summary of the topology of structured data.
method Expected Persistence Diagram (EPD) and its quantization.
result Optimal estimation of EPD with near-optimal quantization.
New bandit algorithms focus on extreme values, outperforming existing methods.
problem Optimizing decisions based on extreme values rather than expected values.
method Robust statistics-based algorithms with vanishing extremal regret.
result The proposed algorithms achieve superior performance compared to existing methods.
Kernel for Lévy rough paths derived from PDE system.
problem Computing similarity measures for Lévy rough paths.
method Developed a PDE system for the expected signature of inhomogeneous Lévy processes.
result Gaussian martingales' expected signature kernel satisfies a Goursat PDE.
Expands Bayesian experiment design framework to account for model discrepancies.
problem Model misspecification in Bayesian optimal experiment design.
method Introduces Expected General Information Gain and Expected Discriminatory Information criteria.
result Demonstrates improved robustness and detection capabilities in experiment design.
Ineffective risk measures fail to control risky investor behavior in markets with arbitrage opportunities.
problem Ineffectiveness of coherent risk measures in managing risky investor behavior in markets with arbitrage opportunities.
method Analytical determination of ρ-arbitrage portfolios and consideration of realistic numerical examples of incomplete markets. result Expected shortfall constraints can be ineffective in realistic markets, but reasonable expected utility constraints are effective.
Federated learning limits and optimal algorithm with low communication cost.
problem Achieving optimal performance in one-shot federated learning with limited communication.
method Investigates the impact of communication constraints on expected error, proposes Multi-Resolution Estimator (MRE).
result MRE achieves error close to theoretical limit with B≥logmn and is order optimal. Quantum algorithm for dynamic asset allocation using expected shortfall.
problem Dynamic risk management in finance, especially tail risks.
method Quantum annealing algorithm in QUBO form for expected shortfall constraint.
result Quantum algorithm provides a faster solution for dynamic asset allocation.
We introduce the truncated Gaussian graphical model (TGGM) as a novel framework for designing statistical models for nonlinear learning. A TGGM is a Gaussian graphical model (GGM) with a subset of variables truncated to be nonnegative. The truncated variables are assumed latent and integrated out to induce a marginal m…
Develops unbiased estimation method using underdamped Langevin dynamics.
problem Estimating expectations of non-negative Lebesgue density probability measures.
method Underdamped Langevin dynamics, time-discretized versions, doubly randomized estimation.
result Proves finite variance and expected/finite cost of the proposed estimator.