Extends inequality for Rademacher complexities using p-stable variables.
problem Improving Rademacher complexity bounds using p-stable variables. method Extends contraction inequality to p-stable variables for 1<p<2. result New bounds for Rademacher complexities with p-stable variables. The cohomology of complex irreducible polynomials stabilizes with degree or variables.
problem Understanding the cohomology of complex irreducible polynomials.
method Proving homological stability in cohomology as degree or variables increase.
result Cohomology stabilizes with respect to both degree and number of variables.
The paper constructs a complex for the Dirac operator in 4 dimensions.
problem Constructing a complex for the Dirac operator in 4 dimensions.
method Using the Penrose transform, the paper constructs a relative BGG complex and its direct image.
result An explicit construction of a complex starting with the Dirac operator in any number of variables.
A method to assess variable importance in complex predictive models.
problem Assessing the importance of variables in complex predictive models.
method Assigning relevance measures to each variable by comparing predictions with a ghost variable and analyzing joint effects.
result The method provides insights into variable importance and joint effects not available with other methods.
New algorithm for learning RBMs with sparse latent variables.
problem Learning RBMs with sparse latent variables efficiently.
method Algorithm with time complexity O(n^(2^s+1)) for sparse RBMs.
result Improves learning time for RBMs with sparse latent variables.
New method models complex dynamics using a base variable.
problem Modeling complex high-frequency dynamics from time series.
method Constructing a joint model with a base variable and a target variable.
result Successfully models chaotic behavior and reconstructs statistical properties.
StructureBoost improves gradient boosting for complex categorical variables efficiently.
problem Efficiently handling complex categorical variables with known structure.
method Two methods to overcome computational obstacles in SCDT enumeration for structured categorical variables.
result StructureBoost outperforms existing packages on complex categorical problems.
The paper proposes methods to extract and analyze individual variable information from complex dependencies.
problem Analyzing and understanding complex dependencies between multiple variables.
method Reversible normalization and iterative dependency reduction to extract individual information, and use it for direct mutual information and multi-feature Granger causality analysis.
result Decoupling of variables to analyze their individual information and direct mutual information transfers.
New sampler reduces MCMC complexity for Bayesian variable selection.
problem High-dimensional Bayesian variable selection with high computation complexity.
method Variable-complexity subset weighted-Tempered Gibbs Sampler (wTGS) with Rao-Blackwellized estimator.
result Variances of Rao-Blackwellized estimator are smaller than those of subset wTGS.
We give some characterizations for the critical values at infinity of a rational function in two complex variables in terms of the Euler characteristic, the Malgrange condition and the M-tameness
Method infers causal direction using data discretization and complexity calculation.
problem Determining causal direction between continuous variables.
method MDL Binning technique for data discretization and complexity calculation.
result Captures the shape of the data to determine causal direction.
Functions of several octonion variables are investigated and integral representation theorems for them are proved. With the help of them solutions of the ∂~-equations are studied. More generally functions of several Cayley-Dickson variables are considered. Integral formulas of the Martinelli-Bochner,…
Optimized variable orderings improve autoregressive model performance.
problem Challenges in variable ordering affect autoregressive model efficiency.
method Learn graphical model structure to inform optimal variable orderings.
result Graph-informed orderings yield higher-fidelity samples.
Proves new concentration inequalities for sub-gaussian and sub-exponential variables.
problem Understanding functions of independent random variables better.
method Sub-gaussian and sub-exponential conditions, Rademacher complexities, Lipschitz function classes.
result Extension of Rademacher complexities to unbounded sub-exponential distributions.
New MCMC method for complex models with large variables.
problem Inference on posterior model probabilities in large model spaces.
method Reversible genetically modified mode jumping Markov chain Monte Carlo (GMJMCMC).
result Introduced a proper MCMC with correct limiting distribution.
We describe a method to reduce partial differential equations of Monge-Ampère type in 4 variables to complex partial differential equations in 2 variables. To illustrate this method, we construct explicit holomorphic solutions of the special lagrangian equation, the real Monge-Ampère equations and the Plebanski equatio…
SP-SPCA improves sparse PCA by adaptively adjusting variable penalties, enhancing interpretability and stability.
problem Poor interpretability and variable redundancy in PCA for high-dimensional data.
method Introduces a single equilibrium parameter to adaptively adjust variable penalties in the L2 regularization framework.
result Consistently outperforms standard sparse PCA methods in identifying sparse loading patterns and preserving cumulative variance.
Solves Nekhoroshev's problem on invariant tori for Hamiltonian systems with cyclic variables.
problem Finding invariant isotropic tori under Hamiltonian phases flows with involution Hamilton functions.
method Constructs monodromy operator and provides conditions for existence and uniqueness of complex germ without simple spectrum condition.
result Full solution to Nekhoroshev's problem, including Hamiltonian systems with cyclic variables.
Latent variable models improve RL by facilitating efficient learning and exploration.
problem Improving sample efficiency in reinforcement learning.
method Representation view of latent variable models for state-action value functions, incorporating kernel embeddings and UCB exploration.
result Established sample complexity of the proposed approach in online and offline settings, demonstrated superior performance in benchmarks.
Adaptive probabilistic PCA adapts complexity with varying subspaces.
problem Adaptive probabilistic PCA models varying complexity in data.
method Relaxed linear Gaussian model with discrete latent variables, Bayesian nonparametric approach.
result Proposes locally adaptive probabilistic PCA (A-PPCA) for varying subspaces.
In this paper, we study deformations of Brieskorn polynomials of two variables obtained by adding linear terms consisting of the conjugates of complex variables and prove that the deformed polynomial maps have only indefinite fold and cusp singularities in general. We then estimate the number of cusps appearing in such…
Defines new two-variable elliptic genera for manifolds and derives modular forms.
problem Develops new elliptic genera for manifolds.
method Introduces and defines new two-variable elliptic genera for manifolds and derives their properties.
result Derives modular forms from the elliptic genera.
Two Bayesian optimization methods tackle dynamic design spaces with mixed variables.
problem Optimizing complex systems with varying numbers and types of variables and constraints.
method Two Bayesian optimization approaches: budget allocation and kernel function.
result Both methods converge faster and more consistently than standard approaches.
New algorithm learns Bayesian network structures with fewer samples.
problem Learning Bayesian network structures with limited observational data.
method Active sampling strategy to select variables for observation.
result Active algorithm finds structures close to optimal with fewer samples.
We study the computational complexity of Markov chain Monte Carlo (MCMC) methods for high-dimensional Bayesian linear regression under sparsity constraints. We first show that a Bayesian approach can achieve variable-selection consistency under relatively mild conditions on the design matrix. We then demonstrate that t…
Defines a new metric to measure importance of predictors in complex machine learning models.
problem Measuring importance of predictors in black box machine learning models.
method Introduces a new metric, GVIM, based on true conditional expectation functions and causal interpretation.
result The GVIM can be represented as a function of Conditional Average Treatment Effect (CATE), providing a causal interpretation.
Proposes PEID for analyzing synergistic causation in complex systems.
problem Challenges in identifying and analyzing synergistic causation in complex systems.
method Partial Effective Information Decomposition (PEID) framework.
result Unified and computable characterization of synergistic causal relations.
Two statistical tasks are shown to have equivalent sample complexity.
problem Determining if a function depends on only a few variables and identifying those variables.
method Proved statistical equivalence of feature selection and junta testing through sample complexity analysis.
result Brute-force algorithm is sample-optimal for both tasks with optimal sample size.
Energy trees handle complex data structures with multiple variable types.
problem Handling intricate data structures with various types of covariates.
method Energy trees, a regression and classification model, use energy statistics to accommodate structured covariates of different types.
result Energy trees maintain statistical foundations, interpretability, and robustness to overfitting.
Improved clustering speed for 20 clusters on CIFAR-100 dataset.
problem Training time complexity for VAEs with discrete latent variables is linear in the number of clusters.
method Applied a continuous relaxation to discrete variables in Gaussian Mixture VAE, reducing training time complexity to constant.
result Reduced training time from 47 hours to 6 hours for 20 clusters on CIFAR-100.
Hierarchical-CPI improves variable importance measurement for medical data.
problem Limited interpretability of complex medical models.
method Hierarchical-CPI measures conditional variable importance with statistical control, handling correlated data.
result Hierarchical-CPI outperforms existing methods in medical datasets.
In this paper we give definitions of matrix rates of return which do not depend on the choice of basis describing baskets. We give their economic interpretation. The matrix rate of return describes baskets of arbitrary type and extends portfolio analysis to the complex variable domain. This allows us for simultaneous a…
Unified framework for modeling hierarchical spaces in design problems.
problem Challenges in modeling hierarchical, conditional, heterogeneous, or tree-structured domains.
method Unified framework combining feature modeling and graph theory, introducing meta and partially-decreed variables.
result Demonstrated effectiveness on complex system design problems, including neural networks and green-aircraft.
For a complex polynomial in two variables we study the morphism induced in homology by the embedding of an irregular fiber in a regular neighborhood of it. We give necessary and sufficient conditions for this morphism to be injective, surjective. Particularly this morphism is an isomorphism if and only if the correspon…
Future autonomous systems need reliable world models and complex action sequences.
problem Current automated systems lack reliable world models and complex action sequences.
method Introduce energy-based and latent variable models combined in a hierarchical joint embedding predictive architecture (H-JEPA).
result Combining energy-based and latent variable models in H-JEPA can lead to reliable world models and complex action sequences.
iKF method uncovers complex variable interactions for scientific discovery.
problem Limited interpretability of existing models in decision-making applications.
method Iterative Kings' Forests (iKF) method to uncover multi-order interactions.
result iKF provides strong interpretive power for explainable modeling.
New methods for selecting variables in complex biomedical data.
problem Selecting important variables in multivariate, functional, and complex biomedical data.
method Optimization-based variable selection methods for various regression models.
result Outperforms state-of-the-art methods in accuracy and speed.
Learning in the latent variable model is challenging in the presence of the complex data structure or the intractable latent variable. Previous variational autoencoders can be low effective due to the straightforward encoder-decoder structure. In this paper, we propose a variational composite autoencoder to sidestep th…
We describe a method that infers whether statistical dependences between two observed variables X and Y are due to a "direct" causal link or only due to a connecting causal path that contains an unobserved variable of low complexity, e.g., a binary variable. This problem is motivated by statistical genetics. Given a ge…
When can reliable inference be drawn in the "Big Data" context? This paper presents a framework for answering this fundamental question in the context of correlation mining, with implications for general large scale inference. In large scale data applications like genomics, connectomics, and eco-informatics the dataset…
MTHetGNN models complex relations in multivariate time series forecasting.
problem Complex relations among variables in multivariate time series forecasting.
method Designs a relation embedding module and a temporal embedding module, using graph neural networks and CNNs.
result Achieves state-of-the-art results in multivariate time series forecasting.
Richer prior for neural networks with correlated weights.
problem Weak priors limit neural network complexity and flexibility.
method Latent variables represent network units, conditional weights.
result Richer meta-representations and representations.
Bayesian non-linear latent variable modeling for complex data.
problem Inference for GPLVMs is computationally limited and often leads to overfitting or underestimates uncertainty.
method Approximate Gaussian process mappings with random Fourier features for MCMC inference.
result Generalized RFLVMs perform well on various data types and applications.
Simplified calculus for semimartingales makes complex transformations easier.
problem Complex transformations of semimartingales.
method Unified treatment of transformations for real and complex semimartingales.
result Unified calculus for semimartingales simplifies various transformations.
Extends VAEs to handle complex Bayesian network structures.
problem Handling complex dependency structures in Bayesian networks.
method Extends VAEs with graphical residual flows to model arbitrary dependency structures.
result Demonstrates improved performance on synthetic datasets.
Probabilistic graphical models offer a powerful framework to account for the dependence structure between variables, which is represented as a graph. However, the dependence between variables may render inference tasks intractable. In this paper we review techniques exploiting the graph structure for exact inference, b…
Proves volume conjecture for twist knots using complex analysis.
problem Volume conjecture for twist knots.
method Equivalence relation, complex analysis, analytic continuation, function of several complex variables.
result Proves volume conjecture for twist knots.
We consider N Bernoulli random variables, which are independent conditional on a common random factor determining their probability distribution. We show that certain expected functionals of the proportion LN of variables in a given state converge at rate 1/N as N→∞. Based on these results, we …