Deep neural networks converge to Gaussian mixtures as layer width increases.
problem Understanding the distribution of outputs from deep neural networks.
method Proof and experiments with a simple model showing the convergence of neural network outputs to Gaussian mixtures.
result Neural networks converge to Gaussian mixtures as the width of the last hidden layer increases.
A Bayesian filtering algorithm is developed for a class of state-space systems that can be modelled via Gaussian mixtures. In general, the exact solution to this filtering problem involves an exponential growth in the number of mixture terms and this is handled here by utilising a Gaussian mixture reduction step after …
A tutorial on various methods for clustering longitudinal data.
problem Identifying groups with different trends in longitudinal data.
method Group-based trajectory modeling, growth mixture modeling, longitudinal k-means.
result Strengths, limitations, and model extensions of the methods are discussed.
EnEMF uses Epanechnikov kernel for high-dimensional filtering, improving accuracy and robustness.
problem Suboptimal Gaussian mixture kernel density estimates in high-dimensional settings.
method Ensemble Epanechnikov mixture filter (EnEMF) using optimal Epanechnikov kernel.
result EnEMF reduces error per particle on high-dimensional systems like Lorenz '96.
Bayes-assisted confidence sequences improve efficiency for bounded means.
problem Efficient uncertainty quantification for bounded IID means without parametric assumptions.
method Bayesian working predictive model selects adaptive martingale updates maximizing predictive log-growth.
result Asymptotically log-optimal performance with informative priors reducing width and sampling effort.
Gradient method converges locally linearly for overparameterized Gaussian mixtures.
problem Learning Gaussian mixtures under overparameterization.
method Gradient-based method alternating short descent steps and long Polyak steps.
result Gradient method converges locally linearly to minimizers.
The exponential growth of complex data demands fully automatic clustering. Gaussian mixture models (GMMs) provide uncertainty-aware grouping but often require expertise to specify hyperparameters, e.g., component count and covariance structure. While mclust (R) automates this via Bayesian Information Criterion (BIC), P…
Framework generates realistic crop images for growth modeling.
problem Modeling crop growth over time with precision and detail.
method Two-stage framework: image prediction and growth estimation models.
result Framework accurately predicts crop images with varying conditions.
Method for initializing Gaussian mixtures for variational inference with multi-modal distributions.
problem Challenges in variational inference with Gaussian mixtures due to multimodality and nonconvex loss functions.
method Optimization to find local maxima, local Gaussian approximations, and constrained least squares regression.
result Robust initialization improves variational inference performance and scalability.
New CRM models for sparse networks with linear edge growth.
problem Modeling extremely sparse networks with tractable properties.
method Introduced a new class of CRMs with index of variation α∈(0,1] based on mixtures of stable or generalized gamma processes.
result Models produce networks with near-linear edge growth, aligning with empirical evidence.
Paper examines global Covid-19 data complexity and finds low intrinsic dimensions.
problem Understanding the complexity of Covid-19 data across countries.
method Used a Bayesian mixture model (Hidalgo) to estimate intrinsic dimensionality.
result Covid-19 data projects onto two low-dimensional manifolds without significant loss of information.
Inpatient care is a large share of total health care spending, making analysis of inpatient utilization patterns an important part of understanding what drives health care spending growth. Common features of inpatient utilization measures include zero inflation, over-dispersion, and skewness, all of which complicate st…
Understanding the dynamics of brain tumor progression is essential for optimal treatment planning. Cast in a mathematical formulation, it is typically viewed as evaluation of a system of partial differential equations, wherein the physiological processes that govern the growth of the tumor are considered. To personaliz…
This paper explores how combining quantitative factors and news from LLMs improves stock return prediction.
problem Improving stock return prediction using quantitative factors and news.
method Introduces a fusion learning framework to learn unified representations from factors and LLM-generated newsflow, comparing combination, summation, and attentive methods. Explores mixture models and decoupled training approaches.
result Effective multimodal modeling of factors and news improves stock return prediction and selection.
GMMSEQ clusters AE data streams, identifying cluster onsets and growth.
problem Clustering unlabeled AE data with onsets and growth information.
method Modified Gaussian Mixture Models (GMM) with an objective function for AE timestamps.
result GMMSEQ provides better cluster characterization than standard methods.
This work presents an empirical study of the evolution of the personal income distribution in Brazil. Yearly samples available from 1978 to 2005 were studied and evidence was found that the complementary cumulative distribution of personal income for 99% of the economically less favorable population is well represented…
We study multistep Bayesian betting strategies in coin-tossing games in the framework of game-theoretic probability of Shafer and Vovk (2001). We show that by a countable mixture of these strategies, a gambler or an investor can exploit arbitrary patterns of deviations of nature's moves from independent Bernoulli trial…
Optimization algorithms and Monte Carlo sampling algorithms have provided the computational foundations for the rapid growth in applications of statistical machine learning in recent years. There is, however, limited theoretical understanding of the relationships between these two kinds of methodology, and limited unde…
Enhances mixture models with classifier-defined weights.
problem Density evaluation and sampling in mixture models.
method Introduces Classifier Weighted Mixtures (CWM) with functional weights.
result Improves expressivity in variational estimation without increasing complexity.
We prove a conjecture about approximating Gaussian Processes on one dimension.
problem Computational scaling issues with Gaussian Processes on one dimension.
method Developed a new family of state-space models (LEG) to approximate any stationary GP on one dimension.
result Proved that any stationary GP on one dimension can be approximated using the LEG family.
Optimal mixtures of generative models outperform individual models on image datasets.
problem Selecting the best single model from a group of trained generative models.
method Formulated a quadratic optimization problem and proposed the Mixture-UCB algorithm for efficient selection.
result Mixture of generative models achieves better evaluation scores than individual models on benchmark datasets.
New bounds on sample size for identifying mixture models with grouped samples.
problem Identifying mixture models with minimal sample size.
method Generalized identifiability bounds for mixture models with grouped samples.
result Identifiability with (2m−1)/(k−1) samples per group, with no improvement possible. We consider unsupervised estimation of mixtures of discrete graphical models, where the class variable corresponding to the mixture components is hidden and each mixture component over the observed variables can have a potentially different Markov graph structure and parameters. We propose a novel approach for estimati…
Spatially constrained Gaussian mixture models reduce covariance complexity.
problem High dimensionality in finite mixture models for spatial data.
method Spatial covariance constraint with only four free parameters.
result Improves clustering of multi-way spatial data and inference of spatial patterns.
When estimating finite mixture models, it is common to make assumptions on the mixture components, such as parametric assumptions. In this work, we make no distributional assumptions on the mixture components and instead assume that observations from the mixture model are grouped, such that observations in the same gro…
Improved VB algorithm for NIG mixtures outperforms Gaussian mixtures for non-Gaussian data.
problem Clustering non-Gaussian data, especially heavy-tailed and asymmetric.
method Proposed an improved VB algorithm for NIG mixture models and extended Dirichlet process mixture models.
result Outperforms Gaussian mixtures and existing NIG mixture models, especially for highly non-normative data.
The two most extended density-based approaches to clustering are surely mixture model clustering and modal clustering. In the mixture model approach, the density is represented as a mixture and clusters are associated to the different mixture components. In modal clustering, clusters are understood as regions of high d…
Estimates growth loss in fund models and proposes a shrinkage method.
problem Estimating growth loss in fund models under frequentist and Bayesian estimation.
method Proposes a shrinkage method to target maximal growth with minimal deviation.
result Empirical evidence shows shrinkage gives a stable estimate closer to growth potential.
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…
Paper establishes universal lower bounds and optimal rates for clustering sub-exponential mixture models.
problem Achieving optimal error rates in clustering sub-exponential mixture models.
method Establishes universal lower bounds and demonstrates iterative algorithms' optimality in sub-exponential mixture models.
result Iterative algorithms achieve the universal lower bound in sub-exponential mixture models.
A new method for fast Bayesian mixture model estimation.
problem Estimating Bayesian mixture models is computationally challenging.
method Amortized Bayesian Inference (ABI) framework for mixture models.
result The method provides fast inference for mixture models.
Study improves dividend discount model using VAR process.
problem Improving dividend discount models for better predictions.
method Introduced a Gordon growth model based on Vector Autoregressive Process (VAR).
result Two Propositions related to the new model.
The paper uses Gaussian mixture models for Bayesian networks and proposes an optimization algorithm.
problem Modeling nodes in Bayesian networks with complex distributions.
method Gaussian mixture models combined with double iteration algorithm.
result The double iteration algorithm optimizes Gaussian mixture models effectively.
A new method detects outliers using ensembles of Dirichlet process mixtures.
problem Challenges in unsupervised outlier detection using Dirichlet process mixtures.
method Ensembles of Dirichlet process Gaussian mixtures with random subspace and subsampling.
result Empirically outperforms existing approaches in unsupervised outlier detection.
Deep learning is a hierarchical inference method formed by subsequent multiple layers of learning able to more efficiently describe complex relationships. In this work, Deep Gaussian Mixture Models are introduced and discussed. A Deep Gaussian Mixture model (DGMM) is a network of multiple layers of latent variables, wh…
Paper uses Gaussian mixture models and Wasserstein distance for schema matching.
problem Schema matching between different datasets.
method Gaussian mixture models and Wasserstein distance for comparison.
result Derives an approximation for Wasserstein distance between Gaussian mixture models.
Enhanced Gordon growth model for valuing financial products.
problem Valuation of financial products with time-varying interest rates and dividends.
method Dynamic Gordon growth model with time-varying spot interest rate and dividends, risk-neutral valuation, locally risk-minimizing strategy.
result Pricing and hedging formulas for dividend-paying European options and equity-linked life insurance products.
Bayesian approach learns nonparametric mixture components from heterogeneous data.
problem Realistic modeling of heterogeneous data populations with nonparametric mixture components.
method Bayesian nonparametric modeling using Dirichlet process mixture priors.
result Posterior contraction rates for component densities are nearly polynomial, improving over deconvolution methods.
SMT trains generative models by estimating mixture scores, outperforming existing methods.
problem Training one-step generative models efficiently and effectively.
method Score-of-Mixture Training (SMT) estimates the score of mixture distributions between real and fake samples.
result SMT/SMD outperform existing methods on CIFAR-10 and ImageNet 64x64 datasets.
New method estimates mixture model components efficiently.
problem Estimating the number of components in finite mixture models.
method Group-Sort-Fuse (GSF) procedure for simultaneous estimation of order and mixing measure.
result GSF achieves consistent estimation of true mixture order and n−1/2 convergence rate. New method for summarizing Bayesian mixture models using sliced Wasserstein distances.
problem Estimating the mixing measure in nonparametric Bayesian mixture models.
method Decision-theoretic approach using sliced Wasserstein distances for Gaussian mixtures.
result Effective estimation of the mixing measure and mixture density.
Finite mixture models are statistical models which appear in many problems in statistics and machine learning. In such models it is assumed that data are drawn from random probability measures, called mixture components, which are themselves drawn from a probability measure P over probability measures. When estimating …
Algorithm estimates nonparametric mixtures from grouped data.
problem Estimating identifiable nonparametric mixture models from grouped observations.
method Oracle inequality for weighted kernel density estimators and general consistency result.
result Consistent estimation of mixture components from grouped observations.
Bubbles are essential in certain economic models with high growth and low interest rates.
problem Asset price bubbles exceeding fundamental values.
method Developed the Bubble Necessity Theorem in economic models with specific growth and interest rate conditions.
result Bubbles are inevitable in certain economic scenarios with high growth and low interest rates.
Mixture modeling is a general technique for making any simple model more expressive through weighted combination. This generality and simplicity in part explains the success of the Expectation Maximization (EM) algorithm, in which updates are easy to derive for a wide class of mixture models. However, the likelihood of…
The paper develops methods to create reliable prediction sets for complex mixture models in high-dimensional data.
problem Building accurate prediction sets for high-dimensional mixture models with feature-dependent weights.
method The authors introduce a debiasing procedure and a novel interval combination strategy to construct valid prediction sets.
result The proposed method provides reliable coverage guarantees for prediction sets in high-dimensional mixture models.
In many European countries the growth of the real GDP per capita has been linear since 1950. An explanation for this linearity is still missing. We propose that in artificial intelligence we may find models for a linear growth of performance. We also discuss possible consequences of the fact that in systems with linear…
Revisits granular models explaining firm growth rates and sizes.
problem Understanding the relationship between firm size and growth rate statistics.
method Developed new theoretical insights linking firm size and growth rate statistics within granular models.
result Growth volatility distribution is size-independent but fat-tailed, challenging granular models.