The book explores universal time-series forecasting using mixture predictors.
problem Sequential probability forecasting in a general setting.
method Mixture predictors combining multiple predictors.
result Universality of mixture predictors in a general probabilistic setting.
A framework uses a mixture of predictors for semi-supervised inference.
problem Limited labeled data, abundant unlabeled data.
method Mixture of Experts (MOE) for semi-supervised inference.
result MOE-powered inference framework achieves smallest possible variance.
Transformers can learn optimal regression mixtures efficiently.
problem Limited adoption of tailored regression methods due to their model-specific nature.
method Constructed a generative process for a mixture of linear regressions and used transformers to learn optimal predictors.
result Transformers achieve low mean-squared error and make predictions close to the optimal procedure.
ETM models improve efficiency in semi-supervised logistic regression.
problem Improving efficiency in logistic regression with limited labeled data.
method Developed exponential tilt mixture (ETM) models for semi-supervised estimation.
result ETM-based estimation demonstrates improved efficiency over supervised logistic regression.
NMDR estimates complex mixtures of distributions efficiently.
problem Estimating complex finite mixtures of distributions in high-dimensional settings.
method Flexible additive predictors, neural networks, and deep learning optimizers.
result Competitive performance in complex scenarios compared to existing approaches.
New functional ME models for predicting heterogeneous functional data.
problem Statistical analysis of heterogeneous functional data for prediction.
method Functional Mixtures-of-Experts (FME) models with Lasso-like regularization for sparsity.
result Accurate capture of complex nonlinear relationships and clustering of heterogeneous regression data.
Develops a functional mix-of-experts model for multiclass classification.
problem Multiclass classification with univariate functional predictors.
method Functional mix-of-experts model with regularization and sparsity constraints.
result Regularized maximum likelihood estimation yields interpretable coefficient functions.
Paper proposes mechanism learning to reverse causal inference in ML.
problem Machine learning models learn associational, not causal, relationships.
method Causally weighted Gaussian mixture models (CW-GMMs).
result CW-GMMs can deconfound observational data for reverse causal inference.
Optimal classifiers derived from GMMs are approximated by deep neural networks.
problem Binary classification of high-dimensional overlapping Gaussian mixtures.
method Closed-form expressions for Bayes optimal decision boundaries derived from GMMs' eigenstructure. Empirical validation through synthetic and real-world data.
result Deep neural networks approximate optimal classifiers for GMMs, with decision thresholds related to covariance eigenvectors.
It has been argued that in supervised classification tasks, in practice it may be more sensible to perform model selection with respect to some more focused model selection score, like the supervised (conditional) marginal likelihood, than with respect to the standard marginal likelihood criterion. However, for most Ba…
Paper examines LASSO for high-dimensional predictive regression, improving its performance in forecasting unemployment.
problem High-dimensional predictive regression with many predictors and unit roots.
method LASSO with new probabilistic bounds for consistency.
result LASSO maintains its asymptotic guarantee with standardized predictors and improves forecasting of unemployment.
Mixtures-of-Experts (MoE) are conditional mixture models that have shown their performance in modeling heterogeneity in data in many statistical learning approaches for prediction, including regression and classification, as well as for clustering. Their estimation in high-dimensional problems is still however challeng…
Bayesian framework for analyzing heterogeneous covariance data with a novel MoE-Wishart model.
problem Analyzing complex multivariate systems with varying covariance structures.
method Comprehensive Bayesian framework using mixture-of-experts Wishart model with predictor-dependent mixture weights.
result Accurate subpopulation recovery and estimation in heterogeneous covariance scenarios.
Study how depth affects inference in deep Bayesian neural networks.
problem Understanding how depth impacts inference in overparameterized linear Bayesian neural networks.
method Interpreting finite deep linear Bayesian neural networks as scale mixtures of Gaussian process predictors.
result Advances analytical understanding of how depth affects inference in a simple class of Bayesian neural networks.
Mixtures-of-Experts models and their maximum likelihood estimation (MLE) via the EM algorithm have been thoroughly studied in the statistics and machine learning literature. They are subject of a growing investigation in the context of modeling with high-dimensional predictors with regularized MLE. We examine MoE with …
Proposes a deep generative model for robust forecasting on sparse multivariate time series.
problem Forecasting on sparse multivariate time series with suboptimal results when sparsity is high.
method Dynamic Gaussian Mixture distribution for modeling latent clusters, using neural networks and gating mechanism.
result Demonstrates robust modeling of sparse multivariate time series with improved accuracy.
A new framework uses an Incremental Transformer to design geopolymer mixtures efficiently.
problem Designing geopolymer mixtures with limited data and physical constraints.
method Topology-aware surrogate framework guided by Incremental Transformer.
result The design space is redundant, with fewer effective mixture regimes.
Improves classification of microbiome data using mixture distributions.
problem Challenges in classifying sparse and heterogeneous microbiome count data.
method Distance-based classification using mixture distributions.
result The method outperforms existing distance-based classifiers and machine learning approaches.
This paper tackles model selection for MoE models in high-dimensional data.
problem Model selection for Gaussian-gated localized MoE and block-diagonal covariance localized MoE regression models in high-dimensional data.
method Penalized maximum likelihood estimation framework with non-asymptotic risk bounds.
result Established non-asymptotic risk bounds for model selection in MoE models.
Generative Adversarial Networks (GAN) (Goodfellow et al., 2014) are an effective method for training generative models of complex data such as natural images. However, they are notoriously hard to train and can suffer from the problem of missing modes where the model is not able to produce examples in certain regions o…
Blind source separation (BSS) is one of the most important and established research topics in signal processing and many algorithms have been proposed based on different statistical properties of the source signals. For second-order statistics (SOS) based methods, canonical correlation analysis (CCA) has been proved to…
Method estimates mixture components without discretizing parameters.
problem Learning from mixtures of continuous features with noise.
method Off-the-grid optimization method for continuous parameter space.
result Prediction error bound similar to Lasso predictor.
Bayesian networks learn sub-population differences from data.
problem Inference from a single network structure can be misleading when data populations are heterogeneous.
method A mixture of Bayesian networks where component probabilities depend on individual characteristics.
result Identifies both network structures and demographic predictors of sub-population membership.
Study examines Lasso performance in high-dimensional MoE models.
problem Estimating MoE models in high-dimensional settings with Lasso.
method Investigates SGMoE models with Lasso regularization under mild assumptions.
result Provides non-asymptotic bounds for Lasso regularization parameter.
New method for tensor classification with missing data.
problem Handling incomplete tensor data in high-dimensional classification.
method High-dimensional tensor linear discriminant analysis with TGMM and Tensor LDA-MD.
result Established convergence rates and minimax optimal bounds for misclassification rate.
Amyotrophic Lateral Sclerosis (ALS) is a neurodegenerative disease characterized by a rapid motor decline, leading to respiratory failure and subsequently to death. In this context, researchers have sought for models to automatically predict disease progression to assisted ventilation in ALS patients. However, the clin…
We improve MoE models for classification with rigorous guarantees and practical methods.
problem Limited guarantees for stable maximum-likelihood training and model selection in softmax-gated MoE models.
method Derived a batch MM algorithm with closed-form updates, proved finite-sample rates, and developed a dendrogram selector.
result Achieved near-parametric optimal rates for parameter recovery and improved accuracy over baselines.
New model handles complex non-linear relationships with hidden graph structures.
problem Modeling non-linear relationships with hidden graph-structured interactions.
method Block-diagonal localized mixture of polynomial experts (BLoMPE) regression model with penalized maximum likelihood selection criterion.
result Strong theoretical guarantee for finite-sample oracle inequality.
Mixture of Experts (MoE) are successful models for modeling heterogeneous data in many statistical learning problems including regression, clustering and classification. Generally fitted by maximum likelihood estimation via the well-known EM algorithm, their application to high-dimensional problems is still therefore c…
Unified approach for interpretable regression with flexible modeling.
problem Combining predictive adaptivity with interpretability in heterogeneous data.
method Combining random Fourier features, spectral feature map, principal component analysis, Gaussian mixture model, and cluster-specific generalized additive models.
result Consistently improves upon classical and black-box models across benchmark datasets.
Deep neural networks for ordinal outcomes combining image and tabular data.
problem Lack of interpretable models for ordinal outcomes in mixed data types.
method Ordinal Neural Network Transformation Models (ONTRAMs) integrating DL and classical ordinal regression.
result ONTRAMs achieve performance equivalent to standard multi-class DL models but are faster and more interpretable.
We propose a novel neural sequence prediction method based on \textit{error-correcting output codes} that avoids exact softmax normalization and allows for a tradeoff between speed and performance. Instead of minimizing measures between the predicted probability distribution and true distribution, we use error-correcti…
FlowSDR learns a low-dimensional projection preserving the response's conditional distribution.
problem Learning a low-dimensional projection that captures the response's conditional distribution.
method FlowSDR uses conditional log-likelihood maximization with monotone rational-quadratic spline flows to learn the projection and conditional density.
result FlowSDR outperforms existing SDR methods in various simulation settings and a face-age prediction task.
The application of standard sufficient dimension reduction methods for reducing the dimension space of predictors without losing regression information requires inverting the covariance matrix of the predictors. This has posed a number of challenges especially when analyzing high-dimensional data sets in which the numb…
DAG-FM discovers causal relationships from heterogeneous data.
problem Challenges in causal discovery from heterogeneous causal mechanisms.
method DAG-FM uses two specialized Transformer-based sub-modules and a robust tabular interaction block to model complex row-column interactions.
result DAG-FM achieves state-of-the-art performance on synthetic and real-world datasets.
The dearth of prescribing guidelines for physicians is one key driver of the current opioid epidemic in the United States. In this work, we analyze medical and pharmaceutical claims data to draw insights on characteristics of patients who are more prone to adverse outcomes after an initial synthetic opioid prescription…
The paper proves how Transformers learn from context and generalize well.
problem Understanding how Transformers generalize from diverse tasks.
method Developed a statistical theory for in-context learning, separating risk into Bayes Gap and Posterior Variance.
result The Posterior Variance is task-independent, and the Bayes Gap decreases with more in-context examples.
The problem of developing binary classifiers from positive and unlabeled data is often encountered in machine learning. A common requirement in this setting is to approximate posterior probabilities of positive and negative classes for a previously unseen data point. This problem can be decomposed into two steps: (i) t…
Method provides formal guarantees for decomposing model uncertainty.
problem Decomposing model uncertainty into aleatoric and epistemic components.
method Higher-order calibration using k-snapshots.
result Formal guarantees for aleatoric uncertainty matching real-world distribution.
Recently, there has been significant interest in linear regression in the situation where predictors and responses are not observed in matching pairs corresponding to the same statistical unit as a consequence of separate data collection and uncertainty in data integration. Mismatched pairs can considerably impact the …
We investigate a class of hierarchical mixtures-of-experts (HME) models where exponential family regression models with generalized linear mean functions of the form psi(ga+fx^Tfgb) are mixed. Here psi(...) is the inverse link function. Suppose the true response y follows an exponential family regression model with mea…
PbP strategy improves logistic model prediction with missing values.
problem Predicting with missing inputs in logistic models.
method Pattern-by-Pattern (PbP) strategy for logistic models with missing values.
result PbP accurately approximates Bayes probabilities under GPMM across various missing data scenarios.
The problem of forecasting conditional probabilities of the next event given the past is considered in a general probabilistic setting. Given an arbitrary (large, uncountable) set C of predictors, we would like to construct a single predictor that performs asymptotically as well as the best predictor in C, on any data.…
Proposes a tail-adaptive shrinkage method for robust sparse estimation.
problem Robust Bayesian methods for high-dimensional regression under diverse sparse regimes.
method Global-local-tail (GLT) Gaussian mixture distribution with tail-adaptive shrinkage.
result GLT posterior contracts at minimax optimal rate for sparse normal mean models.
Physical activity levels are an important predictor of cardiovascular health and increasingly being measured by sensors, like accelerometers. Accelerometers produce rich multivariate data that can inform important clinical decisions related to individual patients and public health. The CHAMPION study, a study of youth …
New method for regression in high-dimensional space using mixture modeling and optimal transport.
problem Regression in high-dimensional space with unordered data.
method Mixture modeling and optimal transport for permutation recovery and denoising.
result Explicit upper bounds on mean squared denoising error for Gaussian noise.
New bounds explain deterministic non-smooth deep nets without large Lipschitz constants.
problem Challenges in explaining generalization of deterministic non-smooth deep nets.
method De-randomized PAC-Bayes margin bounds for deterministic non-convex and non-smooth predictors.
result New bounds avoid large Lipschitz constants, providing generalization guarantees.
This paper proposes a method to reduce complexity in GLMs with categorical predictors.
problem Wasteful, hard-to-interpret, and prone to overfitting of traditional one-hot encoding for high-cardinality categorical predictors.
method Clustering categories of categorical predictors through a numerical method that preserves or improves accuracy while reducing the number of coefficients.
result Clustering categories of categorical predictors reduces complexity substantially without harming accuracy.