Sharp lower bound on GHHs' representation power of CPWL functions.
problem Proving the minimum number of nestings for GHHs to represent arbitrary CPWL functions.
method Using a key lemma about finite sums of periodic functions, proving necessity of n nestings.
result Proving necessity of n nestings for GHHs to achieve universal representation power.
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.
Study of loops in sums of Laplace eigenfunctions on surfaces.
problem Uniform bound for the number of nested loops in sums of Laplace eigenfunctions.
method Real-analytic category analysis and biharmonic function construction.
result Uniform bound for the number of rooted double nests in terms of surface, root, and spectral cutoff.
New methods for estimating complex causal effects in econometrics.
problem Estimating causal parameters in short panel data models using nested nonparametric instrumental variable regression.
method Introducing techniques to limit ill-posedness in nested NPIV, providing explicit mean square rates and efficient inference.
result Explicit mean square rates for nested NPIV and efficient inference for causal parameters.
Paper tackles robust model training with a new stochastic algorithm.
problem Training robust models against data distribution shift.
method Derives a novel dual formulation and proposes a nested stochastic gradient descent algorithm.
result Establishes polynomial iteration and sample complexities for large-scale DRO problems.
We develop nested automatic differentiation (AD) algorithms for exact inference and learning in integer latent variable models. Recently, Winner, Sujono, and Sheldon showed how to reduce marginalization in a class of integer latent variable models to evaluating a probability generating function which contains many leve…
This paper uses Nested Sampling to improve Gaussian Process uncertainty quantification.
problem Underestimating predictive uncertainty and overfitting in Gaussian Process models.
method Marginalises hyperparameters using Nested Sampling for spectral mixture kernels.
result Improves predictive performance and uncertainty quantification across various data sets.
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.
Paper tackles robust optimization under uncertainty using nested distance.
problem Optimizing under distributionally robust uncertainty with nested distance.
method Equivalent recursive and dynamic programming reformulations for tractable optimization.
result Optimal robust policies can be found efficiently using convex optimization.
New algorithm tackles nested bi-level optimization problems for robust feature learning.
problem Nested compositional bi-level optimization problems in machine learning.
method Stochastic approximation algorithms for solving nested compositional bi-level optimization problems without matrix inversions.
result Achieves an ε-stationary solution with an oracle complexity of approximately O_T(1/ε^2).
New method for estimating treatment effects without complex propensity models.
problem Estimating treatment effects in dynamic treatment regimes.
method Recursive Riesz representer estimation for de-biasing corrections.
result Directly estimates de-biasing corrections without auxiliary models.
Proposes a method to enforce nestedness in subspace learning methods.
problem Consistency between data representations when choosing different subspaces dimensions.
method Lifts Grassmannian optimization criteria to flag manifolds via nested projectors.
result Successfully addresses the nestedness issue in several machine learning methods.
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.
Deep learning and genetic algorithms speed up cosmological Bayesian inference.
problem Substantial computational demands in Bayesian inference for cosmological parameter estimation.
method Deep learning using feedforward neural networks to approximate likelihood functions dynamically, optimized with genetic algorithms.
result Significant speed-up in Bayesian inference process for cosmological models and datasets.
Adaptive model selection for RL with unknown function classes.
problem Model selection for RL with unknown function classes.
method Proposed adaptive algorithms that adapt to the smallest function class containing the true model.
result Cumulative regret matches that of an oracle with known function classes.
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.
BAxUS optimizes high-dimensional functions adaptively, avoiding performance degradation and failure.
problem State-of-the-art HDBO methods degrade or fail with increasing dimensions.
method BAxUS uses nested random subspaces to adaptively optimize high-dimensional functions.
result BAxUS outperforms state-of-the-art methods across various applications.
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.
Study compares MCMC and nested sampling for high-dimensional physics problems.
problem Efficiently sampling high-dimensional Bayesian posterior distributions in particle physics and cosmology.
method Review and comparison of MCMC and nested sampling techniques on high-dimensional test functions and real physics examples.
result Modern MCMC algorithms can outperform nested sampling in certain cases, highlighting implementation details.
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.
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.
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) samples to achieve an ε-stationary point. Improved MLMC method boosts risk estimation efficiency.
problem Estimating risk measures like Value-at-Risk in financial risk management.
method Novel MLMC parametrization and antithetic sampling.
result Significantly improved performance in practical settings.
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 …
Unified GP model optimizes hyperparameters with conditional dependence.
problem Efficient tuning of hyperparameters in neural networks.
method Unified Bayesian optimization framework based on a new Gaussian process (GP) model.
result Higher prediction accuracy and better optimization efficiency observed.
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…
In science and engineering, intelligent processing of complex signals such as images, sound or language is often performed by a parameterized hierarchy of nonlinear processing layers, sometimes biologically inspired. Hierarchical systems (or, more generally, nested systems) offer a way to generate complex mappings usin…
We study finite-sum nonconvex optimization problems, where the objective function is an average of n nonconvex functions. We propose a new stochastic gradient descent algorithm based on nested variance reduction. Compared with conventional stochastic variance reduced gradient (SVRG) algorithm that uses two reference …
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.
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.
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 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.
By specifying model free preferences towards simple nested classes of lottery pairs, we develop the dual story to stand on equal footing with that of (primal) risk apportionment. The dual story provides an intuitive interpretation, and full characterization, of dual counterparts of such concepts as prudence and tempera…
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.
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.
A new method for efficient nested Monte Carlo simulations in financial modeling.
problem Computational challenges in nested stochastic modeling for financial risk assessment.
method Sample recycling approach to speed up inner loop estimations.
result Significantly more efficient than traditional techniques.
Enhances Bayesian model selection for high-dimensional problems.
problem Bayesian model selection for high-dimensional problems.
method Proximal nested sampling with data-driven priors.
result Improves model selection for log-convex likelihood models.
Nested learning improves model performance on multi-granular tasks.
problem Overconfident models and lack of fine-grained confidence in predictions.
method Introducing nested learning with a sequence of nested feature embeddings and explicit combination of outputs.
result Nested learning outperforms standard end-to-end training on various datasets.
We investigate the problem of computing a nested expectation of the form P[E[X∣Y]≥0]=E[H(E[X∣Y])] where H is the Heaviside function. This nested expectation appears, for example, when estimating the probability of a large loss from a financial portfo…
NEST optimizes deep learning training by placing devices efficiently across networks and memory.
problem Inefficient device placement in distributed deep learning leads to high communication and memory overhead.
method NEST uses network-, compute-, and memory-aware dynamic programming to optimize device placement.
result NEST achieves up to 2.43 times higher throughput and better memory efficiency.
We propose doubly nested network(DNNet) where all neurons represent their own sub-models that solve the same task. Every sub-model is nested both layer-wise and channel-wise. While nesting sub-models layer-wise is straight-forward with deep-supervision as proposed in \cite{xie2015holistically}, channel-wise nesting has…
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.
We present a novel Neural Embedding Spatio-Temporal (NEST) point process model for spatio-temporal discrete event data and develop an efficient imitation learning (a type of reinforcement learning) based approach for model fitting. Despite the rapid development of one-dimensional temporal point processes for discrete e…
This work connects IRL methods from ML and economics.
problem Solving the inverse reinforcement learning problem.
method Shows connections and differences between various IRL methods.
result Identifies key computational and algorithmic differences.
We formalize the notion of nesting probabilistic programming queries and investigate the resulting statistical implications. We demonstrate that while query nesting allows the definition of models which could not otherwise be expressed, such as those involving agents reasoning about other agents, existing systems take …
Parallelizes active learning for Bayesian inference using Nested Sampler.
problem Expensive likelihood evaluations in complex experiments.
method Uses Nested Sampler to generate nearly-optimal batches of candidates in parallel.
result Comparable accuracy to sequential conditioning with efficient parallelization.
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…