NoLimits.jl: Flexible and Composable Nonlinear Mixed-Effects Modeling in Julia
problem Flexible and composable nonlinear mixed-effects modeling
method Macro-based modeling language and unified interface
result Substantially expand the range of nonlinear mixed-effects models
New PDEs of mixed type emerge in fluid mechanics and geometry.
problem Analysis of nonlinear PDEs of mixed type.
method Through historical problems and recent trends.
result Many PDEs are of mixed type, requiring new analysis.
Study on robustness of unsupervised representation learning in slightly misspecified settings.
problem Identify nonlinear representation learning in slightly misspecified settings.
method Formalize and investigate Independent Component Analysis (ICA) with observations generated by a mixing function close to a local isometry.
result Approximate identifiability of nonlinear ICA with almost isometric mixing functions.
Temporal Difference Learning analysis under non-i.i.d. data and nonlinear approximation.
problem Finite-sample behavior of TD(0) under non-i.i.d. data and nonlinear approximation.
method High-probability, finite-sample analysis of vanilla TD(0) on polynomially mixing Markov data, assuming Holder continuity and bounded generalized gradients.
result Bounds on the convergence rate of TD(0) with high probability, matching known i.i.d. rates and holding even with nonstationary initialization.
We consider the problem of recovering a common latent source with independent components from multiple views. This applies to settings in which a variable is measured with multiple experimental modalities, and where the goal is to synthesize the disparate measurements into a single unified representation. We consider t…
A hybrid algorithm combines optimization and enumeration for symbolic regression.
problem Finding any function from a set of operators without prior specification.
method Mixed-integer nonlinear optimization with explicit enumeration and constraints.
result The hybrid algorithm is competitive with state-of-the-art methods.
New approach tackles nonidentifiability in nonlinear blind source separation.
problem Nonidentifiability in nonlinear blind source separation.
method Independent mechanism analysis, incorporating causal assumptions.
result Empirical and theoretical evidence shows improved identifiability.
DDICA separates nonlinear mixed signals robustly.
problem Blind source separation of nonlinear mixed signals.
method Deep deterministic neural network with matrix-based entropy function.
result DDICA effectively separates independent components with high accuracy.
New method identifies latent components in nonlinear mixtures without stringent assumptions.
problem Unraveling latent components in nonlinearly mixed data.
method Constrained autoencoder-based algorithm for identifiability under relaxed assumptions.
result Comprehensive sample complexity results and new identifiability conditions.
In this paper we outline a general method for finding well-posed boundary value problems for linear equations of mixed elliptic and hyperbolic type, which extends previous techniques of Berezanskii, Didenko, and Friedrichs. This method is then used to study a particular class of fully nonlinear mixed type equations whi…
MMbeddings reduces categorical embeddings by treating them as latent effects, significantly decreasing parameters and mitigating overfitting.
problem Large cardinalities in categorical embeddings lead to high parameter counts and overfitting.
method MMbeddings treats embeddings as latent random effects in a variational autoencoder framework, reducing parameter count and mitigating overfitting.
result MMbeddings consistently outperforms traditional embeddings across various tasks, demonstrating its potential in machine learning applications.
Three RFF-based methods for nonlinear causal discovery in mixed data.
problem Nonlinear causal discovery in mixed data with computational constraints.
method FFML, TRFF, and FFCI methods for score-based, constraint-based, and hybrid causal discovery.
result FFML and TRFF methods provide complementary performance in causal discovery.
MPTE uses Transformer attention to estimate mixed-frequency factor models.
problem Estimating factor models in panel datasets with mixed frequencies and nonlinear signals.
method Mixed-Panels-Transformer Encoder (MPTE) with attention mechanisms.
result MPTE achieves competitive performance in nonlinear forecasting environments.
This paper introduces a robust mixing model to describe hyperspectral data resulting from the mixture of several pure spectral signatures. This new model not only generalizes the commonly used linear mixing model, but also allows for possible nonlinear effects to be easily handled, relying on mild assumptions regarding…
Mixed RL improves RL efficiency with dual representations.
problem Poor sampling efficiency in RL methods.
method Uses dual representations of environmental dynamics to search optimal policies.
result Proves convergence and recursive stability of the mixed RL.
New method learns nonlinear systems from single finite trajectory samples.
problem Learning stabilizable nonlinear systems from single finite trajectory samples.
method Gradient-based algorithms with noise-sensitive uniform convergence guarantees.
result Efficient learning of general nonlinear systems with high accuracy and small sample complexity.
The mixed scalar curvature of a foliated Riemannian manifold, i.e., an averaged mixed sectional curvature, has been considered by several geometers. We explore the Yamabe type problem: to prescribe the constant mixed scalar curvature for a foliation by a conformal change of the metric in normal directions only. For a h…
Study adapts β-TCVAE for fMRI to recover nonlinear brain components.
problem Capturing nonlinear brain dynamics in fMRI data.
method Adapted β-TCVAE framework for fMRI data. result Recovery of meaningful nonlinear spatial components in fMRI data.
Independent Component Analysis (ICA) aims to find a coordinate system in which the components of the data are independent. In this paper we construct a new nonlinear ICA model, called WICA, which obtains better and more stable results than other algorithms. A crucial tool is given by a new efficient method of verifying…
We present a global optimization approach for solving the maximum a-posteriori (MAP) clustering problem under the Gaussian mixture model.Our approach can accommodate side constraints and it preserves the combinatorial structure of the MAP clustering problem by formulating it asa mixed-integer nonlinear optimization pro…
New methods for scalable causal discovery from complex data.
problem Learning causal structures from nonlinear, continuous or mixed data.
method BF-BIC score and BF-LRT test for scalable causal discovery.
result BF-BIC score and BF-LRT test enable scalable causal discovery with competitive accuracy and runtime.
Improved state estimation in nonlinear models using amortized backward variational inference.
problem State estimation in general state-space models.
method Amortized backward variational inference with neural network parameters.
result Linear growth of variational approximation error in number of observations.
We introduce 'mixed LICORS', an algorithm for learning nonlinear, high-dimensional dynamics from spatio-temporal data, suitable for both prediction and simulation. Mixed LICORS extends the recent LICORS algorithm (Goerg and Shalizi, 2012) from hard clustering of predictive distributions to a non-parametric, EM-like sof…
New method identifies causal relationships from interventions in complex systems.
problem Learning causal representations from unknown, latent interventions with general nonlinear mixing.
method Strong identifiability results with unknown single-node interventions, using geometric structure of transformed data.
result First instance of causal identifiability from non-paired interventions for deep neural network embeddings.
Stochastic cutting planes improve data-driven optimization speed.
problem Data-driven Mixed-Integer Nonlinear Optimization problems.
method Stochastic version of cutting-plane method.
result Stochastic algorithm converges to ε-optimal solution with high probability.
New method identifies latent components in PNL mixtures without strong assumptions.
problem Identifying latent components in PNL mixtures under unknown nonlinear functions.
method Carefully designed UML criterion to identify a null space associated with the mixing system.
result Identification/removal of unknown nonlinearity under minimal conditions.
New Riemannian optimization improves variance estimation in mixed models.
problem Challenges in estimating variance parameters in linear mixed models due to constraints.
method Formulated as an optimization problem on a Riemannian manifold, using Riemannian gradient and Hessian.
result Yields higher quality variance parameter estimates compared to existing methods.
When considering the problem of unmixing hyperspectral images, most of the literature in the geoscience and image processing areas relies on the widely used linear mixing model (LMM). However, the LMM may be not valid and other nonlinear models need to be considered, for instance, when there are multi-scattering effect…
VNA solves large portfolio optimization problems efficiently.
problem Large-scale portfolio optimization under real-world constraints.
method Mapped to Ising-like Hamiltonian and solved with VNA.
result Identifies near-optimal solutions for over 2,000 assets.
Method generates i.i.d. samples from GT data using space-time mixing.
problem Generating synthetic i.i.d. samples from high-dimensional real-valued distributions.
method Space-time mixing strategies, diffusion bridges, and score-matching.
result Optimal transport from initial to target distribution.
Paper develops methods for estimating gradients of Finslerian Schrödinger equations.
problem Estimating gradients of Finslerian Schrödinger equations.
method Develops new Laplacian comparison theorem and applies it to Finslerian Schrödinger equation.
result Global and local Li-Yau type gradient estimates for positive solutions.
In this paper, we study a class of fully nonlinear metric flow on Kähler manifolds, which includes the J-flow as a special case. We provide a sufficient and necessary condition for the long time convergence of the flow, generalizing the result of Song-Weinkove. As a consequence, under the given condition, we solved the…
Proves regularity of geodesic equation on Hermitian manifolds.
problem Regularity of geodesic equation in mixed volume forms space.
method Ellipticity conditions, uniform Laplacian estimates, explicit subsolutions.
result Existence of unique C1,1 solution to Donaldson equation. GBMixed boosts mixed models for clustered data, estimating mean and variance flexibly.
problem Flexible estimation of mean and variance components in clustered data.
method Gradient Boosting framework for linear mixed models with likelihood-based gradients.
result GBMixed accurately recovers complex nonlinear fixed effects and covariances.
Spectral deconfounding improves machine learning models by reducing hidden confounding effects.
problem Machine learning models can be misled by hidden confounders, leading to unreliable predictions.
method Develops a nonlinear spectral deconfounding framework for gradient boosting that modifies boosting dynamics to slow down in confounding-aligned directions.
result Spectrally deconfounded boosting improves estimation of the target function under hidden confounding and is more scalable.
Incorporating spatial information into hyperspectral unmixing procedures has been shown to have positive effects, due to the inherent spatial-spectral duality in hyperspectral scenes. Current research works that consider spatial information are mainly focused on the linear mixing model. In this paper, we investigate a …
Token-adaptive FFN design improves LLM expressivity.
problem Fixed activation functions limit FFN expressivity in LLMs.
method Mixture of Activations (MoA) and learnable activations (LA).
result MoA achieves lower terminal loss and better scaling than baselines.
The accurate characterization of the business cycles in the nonlinear dynamic financial and economic systems in the time of globalization represents a formidable research problem. The central banks and other financial institutions make their decisions on the minimum capital requirements, countercyclical capital buffer …
Transformers with MLP heads outperform linear baselines in in-context learning.
problem Understanding in-context learning in Transformers with nonlinear MLP heads.
method Analyzing a model with two-layer MLPs trained via gradient steps and fully optimized, under high-dimensional asymptotics.
result Nonlinear MLPs enhance ICL performance, particularly on nonlinear tasks.
This work closes the gap between theory and practice for nICA identifiability.
problem Identifying latent components in nonlinearly mixed data.
method Finite-sample analysis of GCL-based nICA, combining GCL properties, statistical generalization, and numerical differentiation.
result Establishes a trade-off between function learner complexity and expressiveness.
FBMS R package simplifies Bayesian model selection and averaging.
problem Complex regression settings with multi-modal posterior landscapes.
method Efficient MJMCMC and GMJMCMC algorithms for Bayesian model exploration.
result FBMS effectively handles Bayesian generalized linear and nonlinear models.
Derives gradient estimate for a specific nonlinear parabolic equation on Finsler manifolds.
problem Derives gradient estimate for a nonlinear parabolic equation on Finsler manifolds.
method Leverages a new Laplacian comparison theorem to derive a Li-Yau type gradient estimate.
result Establishes a Li-Yau type gradient estimate for the Finslerian logarithmic Schrödinger equation.
Study compares neural and statistical models for Parkinson's disease progression from voice data.
problem Difficult statistical analysis of longitudinal voice biomarkers due to subject correlation, small cohorts, and varied disease trajectories.
method Evaluated Neural Mixed Effects (NME), Generalized Neural Network Mixed Models (GNMMs), and semi-parametric Generalized Additive Mixed Models (GAMMs).
result GAMMs achieve stronger predictive performance and retain interpretable smooth effects and subject-level structure.
New method identifies latent sources from nonlinear mixtures without auxiliary variables.
problem Identifying latent sources from nonlinear mixtures without additional information.
method Structural Sparsity assumptions on the mixing process.
result Latent sources can be identified up to permutation and transformation.
StrADiff separates sources from mixtures without labels, using structured priors.
problem Blind source separation of linear and nonlinear mixtures without labeled data.
method Structured Source-Wise Adaptive Diffusion Framework with Gaussian process priors.
result StrADiff can recover latent source trajectories in an unsupervised manner, especially stable in linear mixtures.
A new method combines machine learning with mixed-effects models for better repeated measurement analysis.
problem Inference of linear coefficients in partially linear mixed-effects models with complex interactions and high-dimensional variables.
method Double machine learning approach to estimate nonparametrically nonlinear variables, then use standard linear mixed-effects techniques to estimate the linear coefficient.
result The estimated fixed effects coefficient converges at the parametric rate and is semiparametrically efficient.
Optimizes marketing strategies with practical constraints.
problem Adjusting marketing activities with minimum and maximum changes.
method Formulated as a mixed integer nonlinear program (MINLP), reformulated for computational efficiency.
result Significant improvements in solution process for realistic problems.
New method discovers causal models from mixed time series data.
problem Discovering causal relationships from heterogeneous time series data.
method Variational inference-based framework MCD for linear and nonlinear causal models.
result Method outperforms state-of-the-art benchmarks in causal discovery tasks.