Unified SGD method improves convergence for nested optimization problems.
problem Stochastic nested optimization problems.
method ALTERNATE dESCEN (ALSET) method leveraging hidden smoothness.
result Requires samples to achieve an -stationary point.
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48 results for “nested types”
Generative model synthesizes complex data structures with composite and nested types.
problem Synthesizing complex data structures with composite and nested types.
method Generic framework using causal transformers for struct and list generation.
result Consistently outperforms state-of-the-art models on standard and complex hierarchical datasets.
New model clusters cells and individuals, revealing genetic influences on cell types.
problem Clustering nested data with group-level and observation-level variables.
method Nested Atoms Model (NAM), Bayesian nonparametric approach.
result Identifies clusters of genetically similar individuals with homogeneous cell-type profiles.
Hidden variables are ubiquitous in practical data analysis, and therefore modeling marginal densities and doing inference with the resulting models is an important problem in statistics, machine learning, and causal inference. Recently, a new type of graphical model, called the nested Markov model, was developed which …
Proposes a Nested Block Model to unify various network block models.
problem Lack of nested structure and differing parameter complexity among block models.
method Formulates a hierarchy of block models (NBM) that includes SBM, DCBM, and PABM as special cases.
result Allows clustering and estimation without preliminary testing, simplifying model selection.
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.
Study quantifies performance gap between tensor and matrix-based approaches in nested matrix-tensor model.
problem Estimating a planted signal in a nested matrix-tensor model.
method Comparing tensor-based and matrix-based approaches for best rank-one approximation of tensor data.
result Derives precise algorithmic threshold for the unfolding approach and shows BBP-type transition behavior.
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 propose Dirichlet Simplex Nest, a class of probabilistic models suitable for a variety of data types, and develop fast and provably accurate inference algorithms by accounting for the model's convex geometry and low dimensional simplicial structure. By exploiting the connection to Voronoi tessellation and properties…
We study the Whitehead torsions of inertial h-cobordisms, and identify various types representing a nested sequence of subsets of the Whitehead group. A number of examples are given to show that these subsets are all different in general.
LSTMs and GRUs are the most common recurrent neural network architectures used to solve temporal sequence problems. The two architectures have differing data flows dealing with a common component called the cell state (also referred to as the memory). We attempt to enhance the memory by presenting a modification that w…
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.
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.
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.
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 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.
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 …
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…
Nested Variational Inferencestat.ML
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.
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.
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.
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 with any prior you likeastro-ph.IM
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.
Nesting behind -invariantsmath.RT
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 -invariants.
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.
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.
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…
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.
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 …
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.
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…
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…
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.
EENNs improve inference efficiency but need nested prediction sets for reliable uncertainty estimates.
problem Non-nested prediction sets from standard uncertainty quantification methods in EENNs.
method Introduced anytime-valid confidence sequences (AVCSs) tailored for EENNs.
result AVCSs generate nested prediction sets across EENN exits, addressing the issue of non-nested sets.
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.
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…
New formulas compare total mean curvatures of nested hypersurfaces.
problem Computing total mean curvatures of nested hypersurfaces.
method Developed differential forms based on Chern's work to compare curvatures.
result Quicker proof of recent result on total mean curvatures.
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.
A system of nested dichotomies is a method of decomposing a multi-class problem into a collection of binary problems. Such a system recursively splits the set of classes into two subsets, and trains a binary classifier to distinguish between each subset. Even though ensembles of nested dichotomies with random structure…
A tree-based dictionary learning model is developed for joint analysis of imagery and associated text. The dictionary learning may be applied directly to the imagery from patches, or to general feature vectors extracted from patches or superpixels (using any existing method for image feature extraction). Each image is …
Study geodesics on nested non-holonomic systems.
problem Interplay between geodesics on related non-holonomic systems.
method Hamiltonian formalism and geometric preliminaries.
result Presented several geometric examples, including exotic spheres and twistor space.
Study improves predictive performance testing for high-dimensional data using exhaustive nested cross-validation.
problem Reproducibility issues in -fold cross-validation for high-dimensional data.
method Proposes a novel predictive performance test based on exhaustive nested cross-validation, addressing computational complexity with a closed-form expression.
result Demonstrates the effectiveness of Ridge-based methods in high-dimensional predictive performance testing.
We show that deliberately introducing a nested simulation stage can lead to significant variance reductions when comparing two stopping times by Monte Carlo. We derive the optimal number of nested simulations and prove that the algorithm is remarkably robust to misspecifications of this number. The method is applied to…