CDVI improves variational inference for survival analysis by considering censoring mechanisms.
problem Challenges in applying variational methods to survival data, especially the dependence on censoring.
method Censor-dependent variational inference (CDVI) tailored for latent variable models in survival analysis.
result Significant improvements in estimating individual survival distributions.
Survey of factor analysis, PCA, variational inference, and VAE.
problem Dimensionality reduction and generative modeling of data.
method Variational inference, factor analysis, probabilistic PCA, and VAE.
result Derivation and explanation of ELBO, EM, and closed-form solutions.
A practical guide to Variational Bayes methods.
problem Bayesian inference for data analysis practitioners.
method Explains and demonstrates commonly used Variational Bayes methods.
result Quick derivation and implementation of VB algorithms.
The paper is mainly devoted to systematic developments and applications of geometric aspects of second-order variational analysis that are revolved around the concept of parabolic regularity of sets. This concept has been known in variational analysis for more than two decades while being largely underinvestigated. We …
Solves wealth maximization problem using variational analysis.
problem Maximizing expected utility of terminal wealth.
method Variational analysis, forward-backward stochastic differential equation (FBSDE).
result Characterization and solutions for various utility functions.
Research in several fields now requires the analysis of data sets in which multiple high-dimensional types of data are available for a common set of objects. In particular, The Cancer Genome Atlas (TCGA) includes data from several diverse genomic technologies on the same cancerous tumor samples. In this paper we introd…
Improved image learning using elliptically contoured tensor-variate distributions.
problem Inadequate statistical analysis for tensor-valued data, especially with heavier or lighter tails.
method Developed a family of elliptically contoured tensor-variate distributions and derived their properties and procedures for estimation.
result Tensor-variate classification rules and tensor-on-tensor regression better predict and characterize data than TVN-based methods.
Constructs surfaces with conical singularities using variational methods.
problem Creating Hamiltonian Stationary Surfaces with specific singularities.
method Variational methods and convergence process similar to Ginzburg-Landau analysis.
result Obtained surfaces with prescribed conical singularities related to optimal Wente constants.
New clustering algorithm for time series data using RNN and variational Bayes.
problem Lack of generative model-based clustering methods for time series data.
method Recurrent Neural Network (RNN) with variational Bayes method.
result Robustness against phase shift, amplitude, and signal length variations.
A complete error analysis of variational integrators is obtained, by blowing up the discrete variational principles, all of which have a singularity at zero time-step. Divisions by the time step lead to an order that is one less than observed in simulations, a deficit that is repaired with the help of a new past-future…
Geometric analysis improves convergence of variational inference.
problem Challenges in analyzing convergence of variational inference due to non-convexity and non-smoothness.
method Exploits exponential family structure and Bregman divergences to geometrically analyze the optimization landscape.
result Establishes non-asymptotic convergence rates for gradient descent algorithms.
VarFA efficiently estimates student skill levels with uncertainty for adaptive testing.
problem Efficiently estimating student skill levels with uncertainty for adaptive testing.
method VarFA uses variational inference to extend factor analysis models for educational data.
result VarFA efficiently handles large datasets and produces uncertainty estimates.
A new model for multiview data analysis using graph autoencoders.
problem Nonlinear multiview canonical correlation analysis for large datasets.
method Variational approach with graph convolutional neural networks.
result Competitive performance on classification, clustering, and recommendation tasks.
This work interprets SFA through variational inference, relaxing linearity constraints.
problem Recover non-linear SFA from variational inference.
method Probabilistic interpretation of SFA through variational inference, relaxing linearity constraints.
result Reinterprets SFA as a variational framework, allowing slowness as a regularizer to reconstruction loss.
In this document we are going to derive the equations needed to implement a Variational Bayes i-vector extractor. This can be used to extract longer i-vectors reducing the risk of overfittig or to adapt an i-vector extractor from a database to another with scarce development data. This work is based on Patrick Kenny's …
Through the direct study of the analysis estimator we derive oracle inequalities with fast and slow rates by adapting the arguments involving projections by Dalalyan, Hebiri and Lederer (2017). We then extend the theory to the square root analysis estimator. Finally, we focus on (square root) total variation regularize…
DICCA maps multi-view data into a shared latent space with interpretable components.
problem Learning from multiple related but distinct data views.
method DICCA extends CCA to deep generative networks and uses sparsity-inducing priors for interpretability.
result DICCA effectively disentangles shared and view-specific variations in multi-view data.
Unified analysis of efficient local training methods for distributed variational inequalities.
problem Efficient distributed/federated learning for variational inequality problems.
method Unified convergence analysis of communication-efficient local training methods.
result First local gradient descent-accent algorithms with improved communication complexity.
NeVI-Cut uses neural networks to efficiently propagate uncertainty without feedback.
problem Efficiently propagating uncertainty in downstream Bayesian analysis without feedback.
method NeVI-Cut combines neural networks and normalizing flows for variational inference.
result NeVI-Cut achieves significant computational gains and higher accuracy than traditional methods.
Fast variational Bayes methods improve geospatial data analysis speed and accuracy.
problem Inaccurate and slow variational Bayes methods for large geospatial data.
method Combination of calculus of variations, closed-form gradient updates, and linear response corrections.
result Comparable accuracy to spNNGP with reduced computational costs and faster speed.
Paper uses non-Euclidean analysis to classify brain structure variations.
problem Classifying joint variations in multi-object brain structures.
method Combines non-Euclidean statistics and non-parametric integrative analysis.
result Effective, robust, and interpretable joint structure found.
New methods for scalable inference in modular models with misspecified sub-models.
problem Model misspecification in multi-modular models complicates evidence combination.
method Variational methods for approximating Cut and SMI posteriors, and Variational Meta-Posterior.
result Feasibility of analysis with multiple cuts using a single set of variational parameters.
Proposes a deep probabilistic multi-view model for multi-view learning.
problem Learning from multiple related views with shared latent structure.
method Probabilistic Canonical Correlation Analysis (CCA) in latent space, deep generative networks, variational inference.
result Efficient variational inference approximates posterior distributions of latent multi-view layer.
We establish new existence and non-existence results for positive solutions of the Einstein-scalar field Lichnerowicz equation on compact manifolds. This equation arises from the Hamiltonian constraint equation for the Einstein-scalar field system in general relativity. Our analysis introduces variational techniques, i…
Several recent works have explored stochastic gradient methods for variational inference that exploit the geometry of the variational-parameter space. However, the theoretical properties of these methods are not well-understood and these methods typically only apply to conditionally-conjugate models. We present a new s…
Improves bandit convex optimization with gradient variations.
problem Bandit Convex Optimization with Gradient Variations.
method Refined analysis of non-consecutive gradient variation.
result Improved dimension dependence for convex and strongly convex functions.
The paper analyzes errors in mechanical systems with external forces.
problem Error analysis of mechanical systems with external forces.
method Analysis of variational integrators with contact order r for discrete mechanical systems. result The contact order of the integrator is the same as the contact order of the original systems.
Many biological data analysis processes like Cytometry or Next Generation Sequencing (NGS) produce massive amounts of data which needs to be processed in batches for down-stream analysis. Such datasets are prone to technical variations due to difference in handling the batches possibly at different times, by different …
Enhances multimodal generation with Normalizing Flows and correlation analysis.
problem Generating coherent cross-modal data from multiple sources.
method Uses Deep Canonical Correlation Analysis for shared information, Normalizing Flows for diversity, and Product of Experts for scalability.
result Improves likelihood, diversity, and coherence in conditional generation.
Extends multivariate regression for tensor-variate data, identifying brain regions and facial characteristics.
problem Challenges in fitting regression models with multivariate responses and covariates.
method Low-rank tensor formats on regression coefficients and tensor-variate normal distribution for errors.
result Maximum likelihood estimators for tensor-on-tensor regression via block-relaxation algorithms.
The paper develops a new approach to conditional risk measures using modular convex analysis.
problem Developing a new method for conditional risk measures.
method Random modular approach to conditional certainty equivalents and niveloids in the conditional L∞-space. result Retrieves a conditional variational formula for optimized certainty equivalents and applies it to the conditional entropic risk measure.
Mathematical analysis shows annealing prevents mode collapse in Gaussian mixtures.
problem Mode collapse in variational inference for multimodal distributions.
method Analyzed annealing strategies for Gaussian mixtures, derived formulas, and tested on neural networks.
result Appropriately chosen annealing schemes can robustly prevent mode collapse.
Harmonic gauge simplifies geometric analysis of Riemannian metrics.
problem Analyzing the Hilbert-Einstein functional and its stability.
method Developed a harmonic gauge to eliminate divergence terms and induce elliptic structure.
result Positivity of curvature operator implies spectral stability of the functional.
SAVAE uses deep learning for survival analysis, improving model performance and interpretability.
problem Complex medical data with censoring and covariate interactions.
method SAVAE is a Variational Autoencoder tailored for survival analysis, using a novel ELBO formulation.
result SAVAE outperforms state-of-the-art techniques in various datasets, demonstrating robustness and interpretability.
Integrative analysis of disparate data blocks measured on a common set of experimental subjects is a major challenge in modern data analysis. This data structure naturally motivates the simultaneous exploration of the joint and individual variation within each data block resulting in new insights. For instance, there i…
Improved accuracy in dynamic response variation analysis using multi-fidelity data fusion.
problem Inefficient characterization of dynamic response variation due to limited high-fidelity data.
method Composite Neural Network fusion approach for multi-level, heterogeneous datasets.
result Improved accuracy in frequency response variation characterization.
VSI model predicts survival distributions efficiently.
problem Predicting time-to-event distributions in clinical applications.
method Variational framework for non-parametric distribution estimation.
result Improved performance over competing solutions.
Tutorial on using neural networks for single cell data analysis.
problem Handling large sequencing datasets efficiently.
method Single cell variational inference using variational auto-encoder.
result Model learns data distribution for insights.
In this work, we develop a novel principal component analysis (PCA) for semimartingales by introducing a suitable spectral analysis for the quadratic variation operator. Motivated by high-dimensional complex systems typically found in interest rate markets, we investigate correlation in high-dimensional high-frequency …
Unified view of GP approximations improves efficiency.
problem Disparate variational features limit GP efficiency.
method View GP as a Banach space to unify feature selection.
result Unified understanding of existing and new features.
Generative model identifies temporal count data components with regime-dependent contributions.
problem Modeling temporal count data with regime-dependent dynamics.
method Generative framework combining regime-adaptive dynamics with Poisson log-normal emissions.
result Established identifiability of the model and revealed co-variation patterns and regime shifts.
Systems of ordinary differential equations (or dynamical forms in Lagrangian mechanics), induced by embeddings of smooth fibered manifolds over one-dimensional basis, are considered in the class of variational equations. For a given non-variational system, conditions assuring variationality (the Helmholtz conditions) o…
The mathematical problem concerning intrinsic storage optimisation is formulated and solved by means of variational analysis. The solution, though obtained in implicit form, still sheds light on many important features of the optimal exercise strategy. It is shown how the solution depends on different constraint types …
The paper improves Gaussian process regression by optimizing hyperparameters.
problem Hyperparameter tuning for Gaussian process regression models.
method Adaptive sparse variational approximations using variational Bayes.
result Minimax optimal rates of convergence for variational posterior.
This paper examines challenges and solutions for solving variational inequalities.
problem Stability issues in solving variational inequalities, especially in multi-objective scenarios.
method Continuous-time analysis to understand and improve stability of algorithms.
result Understanding continuous-time dynamics can help in designing more stable algorithms for variational inequalities.
The paper studies variations of weighted curvature on submanifolds.
problem Variational properties of weighted curvature on submanifolds.
method Analysis of a functional with integrant r-th weighted curvature.
result Applications to hypersurfaces in Euclidean space and the unit sphere.
Improved IFA with Generative Adversarial Networks for high-dimensional latent variables.
problem Limited expressiveness of traditional VAEs in high-dimensional latent variable modeling.
method Introducing Adversarial Variational Bayes (AVB) and Importance-weighted Adversarial Variational Bayes (IWAVB) algorithms.
result IWAVB demonstrated superior expressiveness and higher likelihood compared to IWAE.
Improved sampling method using regularized Stein Variational Gradient Flow.
problem Improving the accuracy of sampling methods in machine learning.
method Proposed Regularized Stein Variational Gradient Flow to interpolate between SVGD and Wasserstein Gradient Flow.
result Established theoretical properties and provided preliminary numerical evidence of improved performance.