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.
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.
Improves test set performance and reduces out-of-sample disappointment for unstable models.
problem Ensuring strong test set performance via cross-validation for unstable models.
method Nested k-fold cross-validation with hyperparameter selection based on a weighted sum of cross-validation metric and model stability measure.
result Improves out-of-sample MSE for sparse ridge regression and CART by 4% and 2% respectively, compared to k-fold cross-validation.
Hierarchical causal models help understand cause and effect in nested data.
problem Learning cause and effect from nested hierarchical data.
method Extend structural causal models and causal graphical models with inner plates, develop graphical identification technique and estimation methods.
result Hierarchical data can enable causal identification even when non-hierarchical data cannot.
A new sampling method estimates scores without training or nested MCMC.
problem Efficient sampling from complex, unnormalised distributions.
method Multiscale averaging in SDEs for score estimation.
result Empirical results show competitive accuracy and efficiency.
We develop a fully Bayesian, computationally efficient framework for incorporating model uncertainty into Type II Tobit models and apply this to the investigation of the determinants of Foreign Direct Investment (FDI). While direct evaluation of modelprobabilities is intractable in this setting, we show that by using c…
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 …
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 …
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.
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.
A novel bootstrap method improves concept drift detection in predictive models.
problem Detecting changes in predictive relationships (concept drift) in data-driven applications.
method Developed a nested bootstrap procedure to calibrate control limits using the entire initial sample.
result The method yields more accurate baseline models and faster CL setup times.
The paper analyzes MACD using operator theory.
problem Understanding the mathematical foundation of MACD.
method Developed a functional-analytic framework interpreting MACD as a phase-corrected, smoothed derivative operator.
result MACD is structurally equivalent to a band-pass filter and can be expressed as a finite difference of delayed and doubly averaged signals.
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.
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…
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 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…
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.
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.
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.
FLDCRF improves sequence labeling performance with latent dynamics interactions.
problem Sequence labeling with improved performance and latent dynamics interactions.
method Factored Latent-Dynamic Conditional Random Fields (FLDCRF) with multiple latent dynamics interactions.
result FLDCRF outperforms state-of-the-art models across multiple datasets.
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.
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 …
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…
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.
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. 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.
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.
Nested dichotomies are used as a method of transforming a multiclass classification problem into a series of binary problems. A tree structure is induced that recursively splits the set of classes into subsets, and a binary classification model learns to discriminate between the two subsets of classes at each node. In …
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.
The scientific method relies on the iterated processes of inference and inquiry. The inference phase consists of selecting the most probable models based on the available data; whereas the inquiry phase consists of using what is known about the models to select the most relevant experiment. Optimizing inquiry involves …
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 this paper, we present UNet++, a new, more powerful architecture for medical image segmentation. Our architecture is essentially a deeply-supervised encoder-decoder network where the encoder and decoder sub-networks are connected through a series of nested, dense skip pathways. The re-designed skip pathways aim at r…
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.
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 …
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 …
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.
Cross-validation estimates model performance on unseen data, not training data.
problem Understanding how cross-validation estimates prediction error and its limitations.
method Analyzing linear models and popular prediction error estimates, introducing nested cross-validation.
result Cross-validation estimates the average prediction error of models fit on other unseen training sets, not the model at hand.
We develop a nested hierarchical Dirichlet process (nHDP) for hierarchical topic modeling. The nHDP is a generalization of the nested Chinese restaurant process (nCRP) that allows each word to follow its own path to a topic node according to a document-specific distribution on a shared tree. This alleviates the rigid, …
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.
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.
A new method sorts models to find the best one with minimal risk.
problem Finding the best model with minimal risk among nested models.
method Nested Empirical Risk (NER) and Sorted NER (S-NER) methods.
result The S-NER method selects the true model order and the most parsimonious model.
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.
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.
The paper improves Monte Carlo methods for optimization problems.
problem Efficiently solving optimization problems with biased Monte Carlo estimators.
method Introduces Multilevel Monte Carlo (MLMC) within Sample Average Approximation (SAA).
result Establishes uniform convergence and sample complexity for MLMC in SAA.
The data torrent unleashed by current and upcoming astronomical surveys demands scalable analysis methods. Many machine learning approaches scale well, but separating the instrument measurement from the physical effects of interest, dealing with variable errors, and deriving parameter uncertainties is often an after-th…
A system of nested dichotomies is a method of decomposing a multi-class problem into a collection of binary problems. Such a system recursively applies binary splits to divide the set of classes into two subsets, and trains a binary classifier for each split. Many methods have been proposed to perform this split, each …
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.