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.
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.
New methods for estimating nested expectations in machine learning.
problem Nested expectations in machine learning and statistics.
method Investigation and analysis of statistical implications of nesting Monte Carlo estimators.
result Established conditions for convergence of nested MC estimators and derived corresponding rates.
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 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.
Improved nested simulation for financial risk measurement.
problem Efficiently estimating nested risk measures in financial engineering.
method Reusing inner simulation outputs to improve efficiency and accuracy.
result The proposed approach outperforms standard nested simulation and regression methods.
New method improves simulation efficiency in high dimensions.
problem Efficiency in estimating functionals of conditional expectations in high dimensions.
method Kernel ridge regression exploiting smoothness of conditional expectation.
result Effective reduction of the curse of dimensionality, bridging convergence rates.
Method combines MLMC and adaptive sampling for efficient risk estimation.
problem Estimating the probability of large losses in financial portfolios.
method Combines MLMC for nested expectations with adaptive sampling.
result Adaptive MLMC method achieves $\mathcal{O}\left( \varepsilon^{-2}|\log\varepsilon|^2
ight)$ complexity.
New method reduces CVA-VaR computation complexity.
problem Efficiently estimating CVA-VaR for financial risk management.
method Multilevel nested simulation for probabilities.
result 3 orders of magnitude reduction in computational complexity.
MLMC boosts Bayesian optimization's look-ahead efficiency.
problem Efficiently computing nested expectations in Bayesian optimization.
method Multilevel Monte Carlo (MLMC) for nested operations.
result MLMC achieves MC convergence rate for nested operations, improving BO performance.
A new algorithm estimates VaR and ES for financial risks.
problem Estimating Value-at-Risk and Expected Shortfall for financial losses.
method Multilevel Stochastic Approximation (MLSA) scheme for nested stochastic approximation problems.
result Optimal complexities for VaR and ES estimation are derived.
Improves predictive performance of nested dichotomies.
problem Improving the performance of multi-class classification problems.
method A simple, general method for improving nested dichotomies produced by random subset selection techniques.
result Improves root mean squared error of nested dichotomies.
There is an increasing interest in estimating expectations outside of the classical inference framework, such as for models expressed as probabilistic programs. Many of these contexts call for some form of nested inference to be applied. In this paper, we analyse the behaviour of nested Monte Carlo (NMC) schemes, for w…
New method solves complex optimization problems with reduced sample complexity.
problem Solving nonconvex stochastic nested optimization problems.
method Stochastic ADMM approach to find ε-stationary points.
result Total sample complexity of O(ε^(-3)) for online case and O((2N_1 + N_2) + (2N_1 + N_2)^(1/2)ε^(-2)) for finite sum case.
We consider probabilistic multinomial probit classification using Gaussian process (GP) priors. The challenges with the multiclass GP classification are the integration over the non-Gaussian posterior distribution, and the increase of the number of unknown latent variables as the number of target classes grows. Expecta…
Study dynamic assortment planning under nested logit models for revenue maximization.
problem Maximize revenue by dynamically selecting assortments of products during a selling season.
method Developed a novel UCB policy that learns and makes decisions based on customers' choice behavior.
result Achieved accumulated regret of i l d e O ( M N T ) ilde{O}(\sqrt{MNT}) i l d e O ( M N T ) with a lower bound of Ω ( M T ) Ω(\sqrt{MT}) Ω ( M T ) . Paper proposes nested MLMC for SNPE with intractable likelihoods.
problem Estimating posterior distributions from intractable likelihoods.
method Nested MLMC for loss function and gradients, with convergence results.
result Effective methods for approximating complex multimodal posteriors.
New method estimates nested expectations with biased and antithetic sampling.
problem Estimating nested expectations with biased and antithetic sampling.
method Nested multilevel Monte Carlo with biased and antithetic sampling.
result Estimator achieves order ε^(-2) asymptotic cost.
Flat cross-validation is as good as nested CV for most classifiers.
problem Selecting the best classification algorithm and its hyperparameters.
method Used flat cross-validation (selecting hyperparams and estimating accuracy in one step) vs nested cross-validation (separate steps).
result Flat cross-validation is computationally cheaper and often selects similar quality algorithms as nested CV.
C-ADAM is a new adaptive solver for complex nested problems.
problem Solving compositional problems involving nested expected values.
method Adaptive solver for non-linear functional nesting of expected values.
result C-ADAM converges to a stationary point in O ( δ − 2.25 ) O(δ^{-2.25}) O ( δ − 2.25 ) . New method for optimizing complex composite functions with reduced variance.
problem Optimizing multi-level composite functions with nested random and smooth mappings.
method Normalized proximal approximate gradient (NPAG) method with nested stochastic variance reduction.
result Total sample complexity of O ( ε − 3 ) O(ε^{-3}) O ( ε − 3 ) in expectation and O ( N + N ε − 2 ) O(N+\sqrt{N}ε^{-2}) O ( N + N ε − 2 ) in finite-sum cases. The paper reduces xVA calculations by approximating sensitivities.
problem Nested expectation problem and computational expense in xVA calculations.
method Polynomial approximations of shocked and unshocked valuation functions, and their difference.
result High accuracy and remarkable computational cost reduction demonstrated.
Develops new optimization techniques for decision-making under uncertainty.
problem Decision-making under uncertainty with complex cost functions and nested expectations.
method Introduces Multistage Conditional Compositional Optimization (MCCO) and develops multilevel Monte Carlo techniques.
result New optimization techniques reduce scenario complexity from exponential to polynomial growth.
Study improves accuracy of risk measures using advanced algorithms.
problem Computing accurate risk measures for financial losses.
method Nested stochastic approximation and multilevel acceleration.
result Established central limit theorems for estimation errors.
Quantum computing offers a quadratic speedup for estimating non-linear functionals.
problem Estimating non-linear functionals of probability distributions.
method Proposes a quantum-inside-quantum Monte Carlo algorithm for a broad class of non-linear estimation problems.
result Achieves a quadratic speedup for non-linear estimation problems, including nested conditional expectations and stochastic optimization.
Proposes categorification of Z-invariants for specific 3-manifolds.
problem Categorification of Z-invariants for negative definite plumbed 3-manifolds.
method Abelian categorification using 3d N=2 theory and log VOAs.
result Nested Weyl-type character formulas reconstruct Z ^ \hat{Z} Z ^ -invariants. Efficiently optimizes expensive functions with multi-step lookahead using one-shot optimization.
problem Optimizing expensive functions with long-term impacts using myopic approaches.
method Formulated as nested optimization problems within a multi-step scenario tree, optimized in one-shot fashion.
result Multi-step expected improvement is computationally tractable and outperforms existing methods.
We propose the use of statistical emulators for the purpose of valuing mortality-linked contracts in stochastic mortality models. Such models typically require (nested) evaluation of expected values of nonlinear functionals of multi-dimensional stochastic processes. Except in the simplest cases, no closed-form expressi…
We accelerate Bayesian inference for neutrino physics experiments by 100-60x.
problem Complex posterior geometries in multi-dimensional parameter spaces.
method GPU acceleration, automatic differentiation, neural-network-guided reparameterization.
result Significant performance improvements in Bayesian inference for direct detection experiments.
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.
Study cobordisms of nested manifolds and their invariants.
problem Understanding cobordisms of nested manifolds and their invariants.
method Identify a nested analog of the Pontryagin-Thom construction and find spaces homotopy equivalent to nested Pontryagin-Thom spaces.
result Discover nested cobordism invariants and provide an alternative proof of Wall's splitting result.
We extend the theory of asymmetric information in mispricing models for stocks following geometric Brownian motion to constant relative risk averse investors. Mispricing follows a continuous mean--reverting Ornstein--Uhlenbeck process. Optimal portfolios and maximum expected log--linear utilities from terminal wealth f…
Scalable tools for nested optimization in deep learning.
problem Solving nested optimization problems on a large scale in deep learning.
method Building scalable tools for bilevel optimization.
result Tools for nested optimization scale to deep learning setups.
New framework improves experimental design using integral probability metrics.
problem Challenges in Bayesian Optimal Experimental Design (BOED) with KL divergence.
method Integrates integral probability metrics (IPMs) for stability and flexibility.
result IPM-based designs yield more robust and accurate credible sets.
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.
Unified SGD method improves convergence for nested optimization problems.
problem Stochastic nested optimization problems.
method ALTERNATE dESCEN (ALSET) method leveraging hidden smoothness.
result Requires O ( ε − 2 ) {\cal O}(ε^{-2}) O ( ε − 2 ) samples to achieve an ε ε ε -stationary point. Let R be an o-minimal expansion of the real field, and let L(R) be the language consisting of all nested Rolle leaves over R. We call a set nested subpfaffian over R if it is the projection of a boolean combination of definable sets and nested Rolle leaves over R. Assuming that R admits analytic cell decomposition, we …
The paper decomposes probabilistic scores into reliability, uncertainty, and information loss.
problem Understanding the reliability and uncertainty of probabilistic predictions.
method Developed decomposition identities for proper losses, quantifying reliability, residual uncertainty, and information gain.
result A three-term identity for classification scores, revealing miscalibration, grouping term, and feature-level uncertainty.
Develops a method for learning proposals in nested importance samplers.
problem Improving sampling quality in complex distributions.
method Nested Variational Inference (NVI) using forward or reverse KL divergence.
result Optimizing nested objectives leads to improved sample quality.
Nested model averaging improves high-dimensional linear regression performance.
problem High-dimensional linear regression with predictor ordering impact.
method Combining model averaging with regularized estimators on the solution path.
result Nested model averaging with lasso and SLOPE outperforms competing methods.
We introduce a novel numerical approach for a class of stochastic dynamic programs which arise as discretizations of backward stochastic differential equations or semi-linear partial differential equations. Solving such dynamic programs numerically requires the approximation of nested conditional expectations, i.e., it…
Nested Slice Sampling accelerates Nested Sampling for GPU acceleration.
problem Challenging inference for complex, multimodal targets.
method Vectorized Nested Slice Sampling using Hit-and-Run Slice Sampling.
result NSS maintains accurate evidence estimates and high-quality posterior samples, robust on multimodal problems.
Gradient-guided nested sampling improves posterior inference efficiency.
problem Efficiently sampling from complex posterior distributions.
method Gradient-guided nested sampling combining differentiable programming, Hamiltonian slice sampling, clustering, mode separation, dynamic nested sampling, and parallelization.
result Significantly faster mode discovery and more accurate partition function estimates.
We investigate the accuracy of the two most common estimators for the maximum expected value of a general set of random variables: a generalization of the maximum sample average, and cross validation. No unbiased estimator exists and we show that it is non-trivial to select a good estimator without knowledge about the …
We formalize nesting in probabilistic queries and correct inconsistent estimates.
problem Inconsistent estimates in probabilistic query nesting.
method Formalized nesting, introduced online nested Monte Carlo estimator, proved correctness and asymptotic variance.
result Corrected inconsistent estimates through new estimator and conditions.
New discrete cobordism category for nested manifolds and relations to algebraic structures.
problem Discrete cobordism category for nested manifolds.
method Stratified Morse theory, Cyl-objects, doubling construction, cylindrical bar construction.
result Relations between Cyl-objects and algebraic structures like Temperley-Lieb algebras.
Nested sampling improved for arbitrary priors.
problem Technical obstacle to using nested sampling with arbitrary priors.
method Parametric bijectors trained on samples from a desired prior density.
result Nested sampling can be used with arbitrary priors.
DNNet slices network for efficient inference.
problem Resource constraints in inference.
method Doubly nested network with channel-wise nesting and channel-causal convolutions.
result Resource-efficient inference with sub-models.