The paper proposes a new portfolio allocation method combining RMT and machine learning.
problem Optimal allocation instability in high-dimensional portfolios.
method Combines Random Matrix Theory covariance estimators with Nested Clustered Optimization.
result The modified NCO algorithm achieves stable allocations without risky short positions.
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.
This study compares and evaluates categorical kernels for Gaussian process regression.
problem Challenges in designing effective categorical kernels for Gaussian process regression.
method Reproducible comparative study of existing kernels, new evaluation metrics, and clustering-based nested kernels.
result Nested kernels outperform other methods, especially when group structure is unknown or unknown.
Model clusters networks and their communities simultaneously.
problem Clustering networks and their communities in unlabeled, heterogeneous networks.
method Nested Stochastic Block Model (NSBM) with Bayesian approach and NDP prior.
result Model accurately estimates both within and across network clustering structures.
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.
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.
A new method using mean shift clustering speeds up Bayesian evidence calculation.
problem Difficulty in Nested Sampling algorithm convergence and systematic errors.
method Mean shift cluster recognition method integrated into NestedFit.
result Significant reduction in computation time and uncertainty of Bayesian evidence.
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. 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 present a Bayesian nonparametric framework for multilevel clustering which utilizes group-level context information to simultaneously discover low-dimensional structures of the group contents and partitions groups into clusters. Using the Dirichlet process as the building block, our model constructs a product base-m…
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.
Hierarchical clustering is a popular method for analyzing data which associates a tree to a dataset. Hartigan consistency has been used extensively as a framework to analyze such clustering algorithms from a statistical point of view. Still, as we show in the paper, a tree which is Hartigan consistent with a given dens…
Paper proposes a tensor model for clustering noisy multi-view data.
problem Clustering noisy multi-view data with non-uniform variances.
method Nested matrix-tensor model for best rank-one approximation.
result Theoretical results predict the exact accuracy of clustering.
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 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.
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.
Study improves portfolio risk estimation methods using robust covariance and CVaR constraints.
problem Improving portfolio risk estimation in the presence of financial data noise and extreme market conditions.
method Exploration of robust covariance estimators, application of CVaR constraints, use of K-means clustering in optimization.
result Robust covariance estimators can outperform market-weighted benchmarks, especially during bull markets.
We consider the problem of analyzing the heterogeneity of clustering distributions for multiple groups of observed data, each of which is indexed by a covariate value, and inferring global clusters arising from observations aggregated over the covariate domain. We propose a novel Bayesian nonparametric method reposing …
We propose a new anytime hierarchical clustering method that iteratively transforms an arbitrary initial hierarchy on the configuration of measurements along a sequence of trees we prove for a fixed data set must terminate in a chain of nested partitions that satisfies a natural homogeneity requirement. Each recursive …
New method uses nested optimal transport for financial time series evaluation.
problem Lack of consensus metric for evaluating generative models in finance.
method Nested optimal transport distance for time-causal tasks, with a parallelizable algorithm.
result Substantial speedups and robustness to financial tasks.
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.
The paper proposes an efficient nested simulation design using likelihood ratio method.
problem Designing nested simulations with fixed outer scenarios and minimizing simulation effort.
method Proposes a bi-level optimization problem to decide inner replications and pooling strategies.
result Optimized design achieves $\cO(Γ^{-1})$ mean squared error of estimators.
This paper considers networks where relationships between nodes are represented by directed dissimilarities. The goal is to study methods that, based on the dissimilarity structure, output hierarchical clusters, i.e., a family of nested partitions indexed by a connectivity parameter. Our construction of hierarchical cl…
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.
t-NEB clusters high-dimensional data hierarchically with density paths.
problem Hierarchical clustering struggles with high-dimensional data.
method t-NEB uses density estimation, maximum density paths, and probabilistic merging.
result t-NEB yields state-of-the-art clustering performance on high-dimensional data.
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 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.
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.
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.
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.
This article introduces proximal planar vortex 1-cycles, resembling the structure of vortex atoms introduced by William Thomson (Lord Kelvin) in 1867 and recent work on the proximity of sets that overlap either spatially or descriptively. Vortex cycles resemble Thomson's model of a vortex atom, inspired by P.G. Tait's …
Driven by the multi-level structure of human intracranial electroencephalogram (iEEG) recordings of epileptic seizures, we introduce a new variant of a hierarchical Dirichlet Process---the multi-level clustering hierarchical Dirichlet Process (MLC-HDP)---that simultaneously clusters datasets on multiple levels. Our sei…
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).
FunCLBM clusters time series data for autonomous driving validation.
problem Validation of autonomous driving systems using large amounts of data.
method FunCLBM model for co-clustering high-dimensional time series data.
result FunCLBM provides structured partition and clustering views of datasets.
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…
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…
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.
Enhances financial risk quantification in classical models.
problem Risk quantification in classical finance models.
method Nested risk measures, limiting behavior analysis.
result Uniqueness of risk-averse limit in classical models.
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.
Optimizes SGD for anytime neural networks, improving accuracy.
problem Training networks that produce increasingly accurate outputs over time.
method Orthogonalized SGD optimizer for nested architectures.
result Significantly improves generalization accuracy of anytime networks.
We discuss some methods to quantitatively investigate the properties of correlation matrices. Correlation matrices play an important role in portfolio optimization and in several other quantitative descriptions of asset price dynamics in financial markets. Specifically, we discuss how to define and obtain hierarchical …
Proposes methods for online conformal prediction with nested prediction sets across multiple confidence levels.
problem Need for uncertainty quantification with multiple confidence levels in diverse applications.
method Online optimization perspective to enforce nestedness of prediction sets while controlling quantile estimation error.
result Achieves stable coverage across all levels, strictly nested prediction sets, and improved efficiency.
Dirichlet Process(DP) is a Bayesian non-parametric prior for infinite mixture modeling, where the number of mixture components grows with the number of data items. The Hierarchical Dirichlet Process (HDP), is an extension of DP for grouped data, often used for non-parametric topic modeling, where each group is a mixtur…
Regionalization is the task of dividing up a landscape into homogeneous patches with similar properties. Although this task has a wide range of applications, it has two notable challenges. First, it is assumed that the resulting regions are both homogeneous and spatially contiguous. Second, it is well-recognized that l…
Many powerful machine learning models are based on the composition of multiple processing layers, such as deep nets, which gives rise to nonconvex objective functions. A general, recent approach to optimise such "nested" functions is the method of auxiliary coordinates (MAC). MAC introduces an auxiliary coordinate for …
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.