Parsimonious neural networks discover interpretable physical laws from data.
problem Discovering interpretable physical laws from data using machine learning.
method Combining neural networks with evolutionary optimization to balance accuracy and parsimony.
result Developed models for classical mechanics and materials melting temperature prediction.
Method selects most useful network model for various tasks.
problem Impact of translating raw data to network models is unexamined.
method Proposes a network model selection methodology focusing on utility and parsimony.
result Demonstrates the importance of network definition for system behavior.
The parsimonious Gaussian mixture models, which exploit an eigenvalue decomposition of the group covariance matrices of the Gaussian mixture, have shown their success in particular in cluster analysis. Their estimation is in general performed by maximum likelihood estimation and has also been considered from a parametr…
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.
Investigates deep hedging under rough volatility models.
problem Performance of deep hedging framework under non-Markovian conditions.
method Analysis of rough volatility models, use of parsimonious network architectures.
result Parsimonious network architectures can capture non-Markovian time-series.
Combining Bayesian nonparametrics and a forward model selection strategy, we construct parsimonious Bayesian deep networks (PBDNs) that infer capacity-regularized network architectures from the data and require neither cross-validation nor fine-tuning when training the model. One of the two essential components of a PB…
Kolmogorov-Arnold Networks offer improved interpretability and parsimony in science tasks.
problem Improving interpretability and parsimony in science-oriented tasks.
method Theoretical analysis of Kolmogorov-Arnold Networks (KAN) with generalization bounds and model complexity.
result Generalization bounds for KAN with various activation functions, scaling with the l1 norm of coefficient matrices and Lipschitz constants. This paper proposes a parsimoniously time varying parameter vector autoregressive model (with exogenous variables, VARX) and studies the properties of the Lasso and adaptive Lasso as estimators of this model. The parameters of the model are assumed to follow parsimonious random walks, where parsimony stems from the ass…
We consider the problem of modeling multivariate time series with parsimonious dynamical models which can be represented as sparse dynamic Bayesian networks with few latent nodes. This structure translates into a sparse plus low rank model. In this paper, we propose a Gaussian regression approach to identify such a mod…
A parsimonious model reduces over-parameterization in skewed matrix variate mixtures.
problem Over-parameterization in skewed matrix variate mixtures.
method Parsimonious family of 256 models using bilinear factor analyzers constrained over clusters, with AECM algorithm for estimation.
result Extensive simulations and real-world datasets (MNIST, Olivetti faces) demonstrate the method's effectiveness.
Enhances KANs for accuracy and interpretability with multi-exit architecture.
problem Unclear optimal depth for KANs and difficulty in optimization and interpretation.
method Introduces multi-exit KANs with each layer having its own prediction branch.
result Multi-exit KANs outperform single-exit versions on various datasets.
Solving for adversarial examples with projected gradient descent has been demonstrated to be highly effective in fooling the neural network based classifiers. However, in the black-box setting, the attacker is limited only to the query access to the network and solving for a successful adversarial example becomes much …
A family of parsimonious shifted asymmetric Laplace mixture models is introduced. We extend the mixture of factor analyzers model to the shifted asymmetric Laplace distribution. Imposing constraints on the constitute parts of the resulting decomposed component scale matrices leads to a family of parsimonious models. An…
A family of parsimonious Gaussian cluster-weighted models is presented. This family concerns a multivariate extension to cluster-weighted modelling that can account for correlations between multivariate responses. Parsimony is attained by constraining parts of an eigen-decomposition imposed on the component covariance …
We introduce a methodology to construct parsimonious probabilistic models. This method makes use of Information Filtering Networks to produce a robust estimate of the global sparse inverse covariance from a simple sum of local inverse covariances computed on small sub-parts of the network. Being based on local and low-…
Proposes a model for identifying edges in low-rank dynamical networks.
problem Inability of conventional methods to handle low-rank dynamical networks.
method Low rank dynamical network model with causal Wiener filtering.
result Consistent method for estimating all network edges.
Proposes a parsimonious graph spectral method for time series data.
problem Efficiently transmitting multivariate time series data.
method Graph spectral embedding with unsupervised, parsimonious encoding.
result Near-linear computational complexity and interpretable event structure.
We propose an elementary model to price European physical delivery swaptions in multicurve setting with a simple exact closed formula. The proposed model is very parsimonious: it is a three-parameter multicurve extension of the two-parameter Hull-White (1990) model. The model allows also to obtain simple formulas for a…
A new model captures financial asset returns' tail behaviors and outperforms GARCH family.
problem Capturing the dynamic tail behaviors of financial asset returns.
method Combines LSTM with a novel parametric quantile function.
result Out-of-sample forecasts of conditional quantiles or VaR outperform GARCH family.
We study "active" decision making over sensor networks where the sensors' sequential probing actions are actively chosen by continuously learning from past observations. We consider two network settings: with and without central coordination. In the first case, the network nodes interact with each other through a centr…
A neural network approach solves dynamic portfolio optimization without dynamic programming.
problem Dynamic portfolio optimization with multiple constraints and high rebalancing frequency.
method Parsimonious neural network without dynamic programming, avoiding high-dimensional expectations.
result Proves convergence to theoretical optimal solution under general conditions.
New framework for network regression models accounting for community structure.
problem Inaccurate modeling of residual dependencies in network regression models.
method Modeling errors as community-based and exploiting exchangeability properties.
result Parsimonious standard errors for regression parameters.
In this paper we consider sparse and identifiable linear latent variable (factor) and linear Bayesian network models for parsimonious analysis of multivariate data. We propose a computationally efficient method for joint parameter and model inference, and model comparison. It consists of a fully Bayesian hierarchy for …
Extracts coarse-grained PDEs from microscopic simulations.
problem Discovering effective PDEs for macro-scale processes from microscopic data.
method Combining neural networks with equation-free numerics and data-driven approaches.
result Efficiently discovers macro-scale PDEs from microscopic simulations.
Neural networks can model chaos efficiently by becoming geometrically chaotic.
problem Lack of theoretical understanding of how neural networks learn chaos.
method Employed a geometric perspective to show neural networks can model chaotic dynamics.
result Neural networks can reconstruct strange attractors and accurately predict local divergence rates.
Improved SINDy autoencoder for identifying noisy dynamical systems.
problem Robust identification of noisy dynamical systems from data.
method Incorporates noise-separating neural network structures into SINDy autoencoder architecture.
result Accurately recovers latent dynamics and estimates measurement noise from noisy observations.
Machine Learning algorithms are increasingly being used in recent years due to their flexibility in model fitting and increased predictive performance. However, the complexity of the models makes them hard for the data analyst to interpret the results and explain them without additional tools. This has led to much rese…
Finite mixtures of regression models offer a flexible framework for investigating heterogeneity in data with functional dependencies. These models can be conveniently used for unsupervised learning on data with clear regression relationships. We extend such models by imposing an eigen-decomposition on the multivariate …
New GMM models fit high-dimensional data with fewer parameters.
problem Overparameterization and lack of flexibility in GMMs for high-dimensional data.
method Piecewise-constant covariance eigenvalue profiles, EM and penalized EM algorithms.
result Superior likelihood-parsimony tradeoffs in density fitting, clustering, and denoising.
We consider the problem of non-parametric regression with a potentially large number of covariates. We propose a convex, penalized estimation framework that is particularly well-suited for high-dimensional sparse additive models. The proposed approach combines appealing features of finite basis representation and smoot…
Bayesian context trees capture complex dependencies in categorical sequences.
problem Complex, long-range dependencies in categorical sequences are not well captured by simple models.
method Parsimonious Bayesian context trees with model-based agglomerative clustering for efficient inference.
result The proposed framework outperforms existing models on real-world data.
Proposes a non-convex optimization method for a parsimonious weighted naive Bayes classifier.
problem Improving naïve Bayes classifier performance with a large number of input variables.
method Sparse regularization of model log-likelihood for direct estimation of variable weights.
result Optimization-based weighted naïve Bayes classifiers achieve equivalent performance to averaging-based classifiers.
New neural network models for complex functional data analysis.
problem Complex relations between functional predictors and responses.
method Function-on-Function regression models using neural networks with continuous hidden layers.
result Demonstrated power and flexibility in handling complex functional models.
Proposes a new framework for predicting stock market movements using sparse neural architectures.
problem Challenging problem of predicting stock market movements using technical indicators.
method Multi-criteria optimization approach to evolve sparse neural architectures.
result Evolved parsimonious networks with better generalization capabilities.
Novel method combines neural network features with survival models for ICU infections.
problem Improving predictive models of ICU infections while maintaining interpretability.
method Semi-parametric approach combining low-resolution and high-resolution data.
result Improved predictive power with interpretability maintained.
A new method reduces high-dimensional data's impact on CWMs using TSNE.
problem High-dimensional data hampers CWMs' accuracy and speed.
method TSNE for dimensionality reduction, parsimonious technique, expectation maximization.
result TSNE enhances CWMs' performance in high-dimensional space.
Let G be a nonabelian, simple group with a nontrivial conjugacy class C⊆G. Let K be a diagram of an oriented knot in S3, thought of as computational input. We show that for each such G and C, the problem of counting homomorphisms π1(S3∖K)→G that send meridians of K to C is al…
GIT-Net uses neural networks to approximate PDE operators efficiently.
problem Approximating PDE operators for complex geometries.
method Parametrizes adaptive generalized integral transforms with deep neural networks.
result GIT-Net outperforms existing neural network operators in multiple areas.
New neural networks model complex phenomena with fewer parameters.
problem Challenges in studying higher-order interactions in neural networks.
method Introducing curved neural networks using the maximum entropy principle.
result Curved neural networks accelerate memory retrieval and exhibit explosive phase transitions.
New method for learning multidimensional CDFs using Archimedean copulas.
problem Learning multidimensional CDFs in high dimensions.
method Generative modeling technique using Archimedean copulas as mixture models with latent variables from neural networks.
result Efficacy and computational efficiency compared to existing methods.
Parsimonious Dynamic Mode Decomposition selects sparse modes robustly.
problem Manual tuning of sparsity parameters in traditional DMD.
method Time-delay embedding and Orthogonal Matching Pursuit.
result Autonomously determines optimally sparse subset of modes.
A new tensor regression model preserves multidimensional data structure.
problem Complex multidimensional data loses intrinsic connections and parameter explosion.
method Developed a parsimonious tensor regression model using Tucker structure and shrinkage penalization.
result The model outperforms benchmark models in forecasting.
Proposes a new approach to approximate maximum likelihood for complex models.
problem Intractable likelihood functions in complex parametric models.
method Simulation-based constrained approximation to the structural model.
result Estimators nearly as efficient as maximum likelihood, feasible in many cases.
Optimal AFs minimize RFR test error and sensitivity.
problem Finding optimal AFs for RFR to minimize test error and sensitivity.
method Closed-form solution for AFs minimizing test error and sensitivity under different functional parsimony.
result Optimal AFs can be linear, saturated linear, or Hermite polynomial expressions.
Novel estimation methods improve MAR model accuracy for high-dimensional time series.
problem Limited estimation techniques for Matrix Autoregressive (MAR) models.
method Adapted Yule-Walker equations and Burg's method.
result Proposed methods achieve comparable model fit to VAR models.
We investigate the detectability of modules in large networks when the number of modules is not known in advance. We employ the minimum description length (MDL) principle which seeks to minimize the total amount of information required to describe the network, and avoid overfitting. According to this criterion, we obta…
MDL principle aids in learning neural network-based causal structures.
problem Learning causal relationships from observations with neural networks.
method Prequential minimum description length (MDL) principle.
result Competitive results on synthetic and real-world data, often recovering correct structure.
Path regularization reveals convex optimization in deep ReLU networks.
problem Understanding the optimization landscape of deep neural networks.
method Introducing path regularization to make the training problem convex and sparsity-inducing.
result Path regularized parallel ReLU networks are a parsimonious convex model in high dimensions.