Develop a variational framework for statistical inference on cyclic interactions.
problem Estimating and comparing large-scale recurrent organization in directed interactions.
method Represent directed interactions as edge flows on a simplicial complex and evolve under an energy-minimizing dynamical system.
result Separate transient interaction components from persistent harmonic flows, yielding a low-dimensional cycle space.
We seek to utilize the nonextensive statistics to the microscopic modeling of the interacting many-investor dynamics that drive the price changes in a market. The statistics of price changes are known to be fit well by the Students-T and power-law distributions of the nonextensive statistics. We therefore derive models…
iLOCO measures feature interactions without assumptions, providing statistical inference.
problem Lack of methods to statistically infer feature interactions.
method iLOCO metric and LOCO inference for distribution-free, efficient computation.
result First inferential approach to detecting feature interactions.
Gaussian process framework learns interaction kernels in multi-species particle systems.
problem Learning interaction kernels in multi-species interacting particle systems from trajectory data.
method Nonparametric Bayesian approach with Gaussian processes.
result Established rigorous statistical guarantees for recoverability and optimality of interaction kernels.
The search for higher-order feature interactions that are statistically significantly associated with a class variable is of high relevance in fields such as Genetics or Healthcare, but the combinatorial explosion of the candidate space makes this problem extremely challenging in terms of computational efficiency and p…
New method finds significant high-order interactions efficiently.
problem Finding statistically significant high-order interactions in high-dimensional data.
method Extends selective inference to high-order interaction models with pruning strategy.
result Demonstrated efficient and powerful method for high-order interactions.
Interpreting neural networks is a crucial and challenging task in machine learning. In this paper, we develop a novel framework for detecting statistical interactions captured by a feedforward multilayer neural network by directly interpreting its learned weights. Depending on the desired interactions, our method can a…
Perfect clustering achieved in hypergraphs with enough interactions.
problem Complexity and lack of tractable models for analyzing hypergraphs.
method Introduced an interaction hypergraph model for analyzing hypergraphs, defined latent embeddings, and analyzed spectral estimators.
result A spectral estimate of interaction latent positions can achieve perfect clustering with enough interactions.
New complexity measure for interactive learning reduces regret to near-optimal levels.
problem Challenges in sample-efficient, adaptive learning algorithms for interactive decision making.
method Introduces the Decision-Estimation Coefficient and the Estimation-to-Decisions (E2D) principle.
result Unified algorithm design principle E2D achieves optimal sample-efficient learning.
Finding statistically significant high-order interaction features in predictive modeling is important but challenging task. The difficulty lies in the fact that, for a recent applications with high-dimensional covariates, the number of possible high-order interaction features would be extremely large. Identifying stati…
A new method detects interactions in neural networks using topological analysis.
problem Detecting interactions between input features in neural networks.
method Topological analysis of neural network connectivity to quantify interaction strength.
result The PID algorithm outperforms state-of-the-art baselines in interaction detection tasks.
Study finds phase transition in context-sensitive language model with short-range interactions.
problem Understanding phase transitions in language models with short-range interactions.
method Constructed a random language model with short-range interactions and investigated its statistical properties.
result Phase transition occurs in context-sensitive language models with constant context length.
We provide sharp empirical estimates of expectation, variance and normal approximation for a class of statistics whose variation in any argument does not change too much when another argument is modified. Examples of such weak interactions are furnished by U- and V-statistics, Lipschitz L-statistics and various error f…
Estimates hypergraphons for modeling complex interactions efficiently.
problem Modeling higher-order interactions using hypergraphons.
method Restricted class of Simple Lipschitz Hypergraphons (SLH) for efficient estimation.
result Optimal rates of convergence for SLH estimator.
As machine learning becomes more pervasive, there is an urgent need for interpretable explanations of predictive models. Prior work has developed effective methods for visualizing global model behavior, as well as generating local (instance-specific) explanations. However, relatively little work has addressed regional …
New method bypasses assumptions for unbiased estimation of complex system interactions.
problem Inferring pair-wise and higher-order interactions from observational data.
method Cross-disciplinary approach using Targeted Learning for unbiased estimation.
result Universal estimator of all-order symmetric interactions without parametric assumptions.
In this study, we investigate the statistical properties of the returns and the trading volume. We show a typical example of power-law distributions of the return and of the trading volume. Next, we propose an interacting agent model of stock markets inspired from statistical mechanics [24] to explore the empirical fin…
New tests detect high-order interactions without permutations.
problem Scalability issues in kernel-based tests for high-order interactions.
method Permutation-free high-order tests using V-statistics and cross-centring.
result Tests yield standard normal distribution under null hypothesis.
New measures and tests for high-order interactions in complex data.
problem Challenges in capturing high-order interactions in multivariate data.
method Hierarchy of d-order interaction measures and kernel-based tests. result Established statistical significance of high-order interactions.
Unified model for interactive estimation with improved learnability measure.
problem Improving learnability in interactive estimation models.
method Introducing a combinatorial measure (dissimilarity dimension) and a general algorithm with polynomial bounds.
result Unified model subsumes statistical-query learning and structured bandits.
Bayesian method reconstructs hidden higher-order interactions from network data.
problem Lack of explicit higher-order interactions in pairwise network data.
method Bayesian approach based on parsimony, infers higher-order structures when statistically supported.
result Demonstrated applicability to various datasets, synthetic and empirical.
New model enhances SPIM for solving low-rank combinatorial optimization and statistical learning problems.
problem Solving large-scale combinatorial optimization problems efficiently.
method Proposed a new computing model for SPIM that can handle low-rank interaction matrices.
result Demonstrated efficient learning, classification, and sampling of MNIST images using the model.
KIPLMC methods improve statistical inference in latent variable models.
problem Statistical inference in latent variable models.
method Joint diffusion process in parameter and latent variable spaces, with two explicit discretizations.
result KIPLMC methods achieve accelerated convergence rates in Wasserstein-2 distance.
Lecture notes on reinforcement learning using statistical methods.
problem Addressing the exploration-exploitation dilemma in decision making.
method Frequentist and Bayesian approaches, function approximation, neural networks.
result Unified framework for decision making and estimation.
In this paper, we propose a hybrid bankcard response model, which integrates decision tree based chi-square automatic interaction detection (CHAID) into logistic regression. In the first stage of the hybrid model, CHAID analysis is used to detect the possibly potential variable interactions. Then in the second stage, t…
We describe and extract time-ordered multibody interactions from complex systems.
problem Complex systems with temporal and multibody dependencies.
method Decompose multivariate Markov chains into time-ordered multibody interactions. Algorithm to extract interactions from data. Measure complexity of interaction ensembles.
result Robust and efficient algorithm to infer time-ordered multibody interactions from data.
I review few conceptual steps in analytic description of topological interactions, which constitute the basis of a new interdisciplinary branch in mathematical physics, "Statistical Topology", emerged at the edge of topology and statistical physics of fluctuating non-phantom rope-like objects. This new branch is called…
Proposes a neural network for recognizing 3D skeleton-based interactions.
problem Recognizing two-person interactions from 3D skeleton sequences.
method Uses Gaussian distributions and Riemannian geometry of SPD matrices and matrix groups.
result Achieves competitive results on three benchmarks for 3D human activity understanding.
A framework infers hyperedges and overlapping communities in hypergraphs.
problem Characterizing the structural organization of hypergraphs with higher-order interactions.
method Statistical inference to infer missing hyperedges and detect overlapping communities.
result Efficient numerical implementation and strong performance on real-world systems.
The method to derive uniform bounds with Gaussian and Rademacher complexities is extended to the case where the sample average is replaced by a nonlinear statistic. Tight bounds are obtained for U-statistics, smoothened L-statistics and error functionals of l2-regularized algorithms.
Unified framework for lower bounds in interactive decision making.
problem Challenges in interactive decision making, especially bandits and reinforcement learning.
method Interactive Fano method and Fractional Covering Number.
result Unified characterization of learnability for stochastic bandit problems and tight lower bounds for interactive decision making.
In many data exploration tasks it is meaningful to identify groups of attribute interactions that are specific to a variable of interest. For instance, in a dataset where the attributes are medical markers and the variable of interest (class variable) is binary indicating presence/absence of disease, we would like to k…
A graph neural network detects beneficial feature interactions for recommender systems.
problem Feature interactions are crucial but not all are beneficial for recommendation accuracy.
method Graph neural network with L0 activation regularization for edge prediction.
result The model outperforms baselines and automatically identifies beneficial feature interactions.
Collaborative Trees model analyzes feature interactions and additive effects.
problem Analyzing complex statistical associations between features and response variables.
method Proposes a novel tree model and its bagging version to decompose mean decrease in impurity and visualize feature contributions.
result Demonstrates the superior capability of the tree model in estimating additive effects and interaction effects.
Automates finding interactions in GLMs using neural networks.
problem Time-consuming and expert-dependent search for GLM interactions.
method Neural networks and model-specific interaction detection method.
result Computational speed improvement over traditional methods.
Proposes a two-stage method for testing variable interactions with FDR control.
problem Testing pairwise interactions in high-dimensional data with dependence.
method Two-stage testing procedure with FDR control using Cramér type moderate deviation technique.
result The proposed method controls FDR and has comparable or improved statistical power.
New framework converts offline to online estimation using black-box offline estimators.
problem Convert offline estimation algorithms to online estimation algorithms.
method Oracle-Efficient Online Estimation (OEOE) framework.
result Achieves near-optimal online estimation error via black-box offline estimators.
New method decomposes KL error using refined information and mode interactions.
problem Learning probability distributions over discrete variables with higher-order interactions.
method Using information geometry, refined mode interactions, and a novel Monte-Carlo sampling technique.
result Complete decomposition of KL error and efficient data use.
2 Diabetes is a leading worldwide public health concern, and its increasing prevalence has significant health and economic importance in all nations. The condition is a multifactorial disorder with a complex aetiology. The genetic determinants remain largely elusive, with only a handful of identified candidate genes. G…
As the availability and importance of temporal interaction data--such as email communication--increases, it becomes increasingly important to understand the underlying structure that underpins these interactions. Often these interactions form a multigraph, where we might have multiple interactions between two entities.…
Following the statistical mechanics methodology, firstly introduced in macroeconomics by Aoki [1996,2002], we provide some insights to the well known works of Greenwald and Stiglitz [1990, 1993]. Specifically, we reach analytically a closed form solution of their models overcoming the aggregation problem. The key idea …
We derive a system of stochastic differential equations simulating the dynamics of the three agent groups with herding interaction. Proposed approach can be valuable in the modeling of the complex socio-economic systems with similar composition of the agents. We demonstrate how the sophisticated statistical features of…
The paper optimizes exceptions in a statistical production system using machine learning.
problem Lack of curated and labeled training data for machine learning in data quality assurance.
method Explainable supervised machine learning to identify and prioritize exceptions.
result Improvement in the quality and efficiency of exceptions generated and authenticated by users.
Renormalization in neural networks linked to quantum field theory.
problem Implementing renormalization in neural networks.
method Mapping neural networks to quantum field theory, applying renormalization techniques.
result Changing weight standard deviation corresponds to a renormalization flow.
Paper develops PAC verification for hypothesis classes and statistical algorithms.
problem Verifying machine learning models interactively.
method Develops interactive proof for PAC verification, proves lower bounds, and introduces a generalization.
result Improved protocol for verifying unions of intervals and statistical query algorithms.
This paper presents a novel study on gas-like models for economic systems. The interacting agents and the amount of exchanged money at each trade are selected with different levels of randomness, from a purely random way to a more chaotic one. Depending on the interaction rules, these statistical models can present dif…
A network-based approach identifies financial factors from asset interactions, explaining market dynamics.
problem Characterizing joint financial asset behavior through underlying drivers.
method Modeling market as coupled iterated maps, where asset returns depend on past returns and interactions.
result Stable patterns of co-movement (financial factors) emerge from asset interactions, explaining asset variance.
Unified approach detects traffic conflicts across various interactions.
problem Inconsistent detection of traffic conflicts across different interactions.
method Unified probabilistic approach decomposes conflicts into statistical learning tasks.
result Effective collision warnings across diverse datasets and environments.