New method infers hidden states in continuous-time phenomena better than traditional models.
problem Traditional HSMM's are limited to discrete time grids and cannot handle irregularly spaced data.
method Formulated integro-differential forward and backward equations for CTSMC's, introduced scalable Viterbi-type algorithm.
result Efficiently solved equations for posterior marginals and path estimates.
Generative models help explore astrophysical phenomena like galaxy evolution.
problem Exploring hypotheses in astrophysics and other areas using data-driven methods.
method Using a neural network to learn a latent space representation of data and generate artificial data to test hypotheses.
result Demonstrated the ability to independently manipulate physical attributes in artificial data.
Tutorial on combining latent variable models with deep learning.
problem Combining latent variable models with deep learning to model natural language.
method Exploring variational inference to address intractable posterior inference and non-differentiability issues.
result Exploration of variational inference techniques to handle deep latent variable models.
Model infers network structure from latent variables.
problem Learning network topology from latent variables and nonlinear data.
method Semi-parametric, non-linear regression model with latent variables.
result Model accurately infers network structure from real data.
Tensor networks improve anomaly detection at LHC for new physics.
problem Identifying new phenomena in proton collision events at LHC.
method Tensor network-based anomaly detection using Matrix Product State with an isometric feature map.
result Tensor networks outperform established quantum methods in identifying new phenomena.
SPACY discovers causal graphs from spatiotemporal data using variational inference.
problem Inferring causal relationships from high-dimensional spatiotemporal data with complex correlations.
method SPACY uses variational inference to model latent time series and their causal relationships, incorporating spatial factors to aggregate correlated data.
result SPACY outperforms state-of-the-art methods on synthetic and real-world data, identifying key causal phenomena.
New method identifies latent relationships in deep models without additional constraints.
problem Latent representations in deep latent variable models are not statistically identifiable.
method Identifies relationships between latent variables (distances, angles, volumes) under mild model conditions.
result Empirically demonstrates more reliable latent distances without additional labeled data.
A new model for time series using discrete latent states.
problem Efficiently modeling time series data with discrete latent states.
method A Markov chain-based model for training high-dimensional discrete latent data.
result Improved performance on time series datasets.
Develops a model to learn shared and idiosyncratic patterns in point processes.
problem Learning shared and unique patterns in point processes from diverse observations.
method Developed a parametric point process model with alternating optimization for learning shared structure and idiosyncratic effects.
result The method yields explainable point process models that perform well compared to existing methods.
Decodes neural activity to assess latent states in real-world driving tasks.
problem Understanding latent states during complex tasks in natural settings.
method Domain-generalized models trained on controlled lab paradigms applied to ecologically valid driving tasks.
result Changes in neural activity correlate with changes in behavior and task performance.
Paper analyzes latent space geometry in generative models using Fisher information.
problem Understanding the structure of latent spaces in generative models.
method Reconstructs Fisher information metric from generated samples and posterior distribution.
result Reveals fractal structure and abrupt changes in Fisher metric at phase boundaries.
The study examines issues with latent distributions in generative models and proposes using Cauchy distribution.
problem Issues with latent distributions causing mismatch in sampled regions during linear interpolations.
method Proposed using multidimensional Cauchy distribution and two methods for creating non-linear interpolations.
result Linear interpolations may generate unrealistic data due to the Central Limit Theorem, and Cauchy distribution mitigates this issue.
Develops SCMs for latent selection to simplify causal analysis.
problem Latent selection complicates causal analysis.
method Introduces a conditioning operation for SCMs to encode latent selection.
result Conditioning operation preserves simplicity, acyclicity, and linearity of SCMs.
The recently developed variational autoencoders (VAEs) have proved to be an effective confluence of the rich representational power of neural networks with Bayesian methods. However, most work on VAEs use a rather simple prior over the latent variables such as standard normal distribution, thereby restricting its appli…
Bayesian model identifies three types of travelers adapting to feedback.
problem Capturing adaptive, feedback-driven travel behavior in heterogeneous individuals.
method Latent Class Reinforcement Learning (LCRL) model with Variational Bayes estimation.
result Three distinct traveler classes identified: context-dependent, persistent exploitative, and exploratory.
Paper proposes NOSTILL-GP for accurate space-time modeling in environmental monitoring.
problem Accurate modeling of space-time dynamics in environmental phenomena.
method NOSTILL-GP - a non-stationary, spatio-temporal Gaussian Process model with efficient training strategies.
result Demonstrates the effectiveness and general applicability of NOSTILL-GP for environmental monitoring.
Causal relationships in time series with latent variables are discovered using LPCMCI.
problem Discovering causal relationships in complex, time-series data with hidden variables.
method Evaluated LPCMCI algorithm for finding generators compatible with multi-dimensional, autocorrelated time series with latent variables.
result LPCMCI performs better than random guessing but is not optimal.
This paper corrects climate model biases using a factor model approach.
problem Systematic biases in GCM outputs due to unobserved confounders.
method Factor model approach to learn latent confounders from historical data and apply them to enhance bias correction.
result Significant improvements in the accuracy of precipitation outputs.
A semi-parametric, non-linear regression model in the presence of latent variables is introduced. These latent variables can correspond to unmodeled phenomena or unmeasured agents in a complex networked system. This new formulation allows joint estimation of certain non-linearities in the system, the direct interaction…
The behaviour of many real-world phenomena can be modelled by nonlinear dynamical systems whereby a latent system state is observed through a filter. We are interested in interacting subsystems of this form, which we model by a set of coupled maps as a synchronous update graph dynamical systems. Specifically, we study …
SPLICE method disentangles shared and private latent variables from multi-view data.
problem Lack of methods to characterize nonlinear relationships and preserve geometric information in multi-view data.
method Neural network-based approach to infer disentangled, interpretable representations of shared and private latent variables.
result SPLICE yields more interpretable representations by preserving geometry and is more robust to incorrect latent dimensionality.
A new algorithm maximizes entropy or mutual information for efficient inference of nonstationary Gaussian processes.
problem Nonstationary dynamics in real-world phenomena pose challenges to accurate modeling.
method LISAL algorithm that adaptively maximizes entropy or mutual information on induced latent dynamics and marginal likelihood.
result Efficient inference of nonstationary Gaussian processes for large-scale real-world applications.
Method detects critical events in complex systems by learning latent causal structure.
problem Detecting onset of epileptic seizures, customer churn, or pandemics from hidden causal interactions.
method A machine learning method that learns an optimal feature representation from powers of the empirical covariance or precision matrix.
result Proves structural consistency and demonstrates competitive results in seizure and churn prediction.
New method improves neural decoding accuracy and reveals latent memory organization.
problem Improving neural decoding of temporal memory organization.
method Bayesian neural decoding using a diversity-encouraging latent representation learning method.
result Substantially higher accuracy in neural decoding and clear latent representation.
This paper shows cross-entropy can recover latent structures in supervised learning.
problem Understanding why supervised learning works well and how models learn interpretable factors of variation.
method Extending identifiability results to parametric instance discrimination, proving cross-entropy minimization can recover latent structures up to linear transformations.
result Models trained with cross-entropy can learn representations of ground-truth factors of variation up to a linear transformation.
The paper explores how equivariant models' biases affect latent representations for better performance.
problem The impact of inductive biases on latent representations in equivariant models.
method Demonstrates the importance of accounting for inductive biases in latent representations of equivariant models.
result Effective invariant projections can be used to retain information in latent representations, improving downstream tasks.
Flexible nonlinear Hawkes processes for time-varying systems.
problem Limited expressive ability of classic Hawkes processes.
method Flexible state-switching Hawkes processes with latent variable augmentation for Bayesian inference.
result Superior performance compared to state-of-the-art competitors.
Paper proposes using semantic spaces and traditional classifiers for sarcasm detection.
problem Sarcasm detection in text, especially on social media.
method Apply classical machine learning algorithms to texts represented in a Latent Semantic space.
result Established reference datasets and baselines for sarcasm detection.
Modeling correlated mutations in cancer for personalized treatment.
problem Identifying mutations for personalized cancer therapy in heterogeneous profiles.
method Proposed correlated zero-inflated negative binomial process with mixed beta-Bernoulli and variational inference.
result Identified biologically relevant correlations between somatic mutations.
This thesis relaxes assumptions for causal discovery, making methods applicable to more complex systems.
problem Learning causal structures from observational data with latent variables.
method Alternative definition of k-Triangle Faithfulness for non-Gaussian distributions and uniform consistency proof.
result Uniform consistency of causal discovery algorithm under modified faithfulness assumption.
The paper argues against the inefficiency of explaining deep learning phenomena.
problem Explaining deep learning phenomena often leads to ad hoc hypotheses.
method Analyzing recent literature to assess the relevance of these phenomena.
result Many phenomena do not appear in real-world applications and may be inefficient.
New model reconstructs cell differentiation paths from single-cell RNA data.
problem Reconstructing dynamic biological phenomena from noisy, heterogeneous, and sparse single-cell RNA-seq data.
method Developed a generative model using Dirichlet diffusion tree and Markov chain Monte Carlo sampler.
result Recovered latent trajectories from simulated single-cell transcriptomes.
LISAL learns nonstationary spatio-temporal models efficiently.
problem Learning nonstationary spatio-temporal models in dynamic environments.
method LISAL uses Gaussian processes to model nonstationary dynamics and latent space changes.
result LISAL reduces computational cost by adaptively sampling latent space dynamics.
The paper studies concentration of measure on manifolds with boundary, focusing on 1-Lipschitz functions.
problem Concentration of measure phenomena of non-negative 1-Lipschitz functions on manifolds with Dirichlet boundary condition. method Examined relation between boundary concentration phenomena and large spectral gap phenomena of Dirichlet eigenvalues of Laplacian. Introduced new invariant called the observable inscribed radius.
result Formulated comparison theorems for the observable inscribed radius under lower Ricci curvature and mean curvature bounds for the boundary.
Sharp changes in time series representing market dynamics are studied by means of the self--similar analysis suggested earlier by the authors. These sharp changes are market booms and crashes. Such crises phenomena in markets are analogous to critical phenomena in physics. A simple classification of the market crisis p…
Study on Lane-Emden equation on curved spaces, revealing new existence and non-existence phenomena.
problem Existence and non-existence of positive solutions for the Lane-Emden equation on Riemannian models.
method Analysis of the subcritical Lane-Emden equation on various Riemannian manifolds with polynomial volume growth.
result Subcritical regime divides into three ranges with distinct existence and non-existence phenomena.
The paper explores higher property T in lattices and its connections to geometric phenomena.
problem Understanding higher property T in lattices and related geometric phenomena.
method Operator-algebraic characterizations of higher property T and connections to lattice geometry.
result Unified framework for understanding higher property T and related geometric phenomena.
This research connects topological changes to cosmic phenomena like black hole formation.
problem Understanding topological changes in cosmic phenomena.
method Using topological surgery and Morse functions to describe changes in 3-manifolds and their fundamental groups.
result New insights into natural phenomena through a topological perspective.
New research shows posterior collapse in VAEs isn't just about KL-divergence.
problem Posterior collapse in Variational Autoencoders (VAEs).
method Analyzes the loss surface of deep autoencoder networks and proves the existence of bad local minima.
result Posterior collapse in VAEs is caused by bad local minima, not just KL-divergence.
Paper connects Stokes phenomena to quantum groups and Poisson-Lie groups.
problem Analyse Stokes phenomena in Poisson-Lie groups and quantum groups.
method Use Ug-valued Stokes phenomena to construct quantum group U_hg and relate it to Poisson-Lie group G*.
result Show that Ug-valued Stokes phenomena can be obtained as a semiclassical limit of the KZ associator.
In this paper we observe that 2-dimensional 0-surgery occurs in natural processes, such as tornado formation and other phenomena reminiscent of hole drilling. Inspired by such phenomena, we introduce new theoretical concepts which enhance the formal definition of 2-dimensional 0-surgery with the observed dynamics. To d…
Novel connections between Neyman-Scott processes and Bayesian nonparametric mixture models enable scalable inference.
problem Efficiently modeling and detecting clusters in spatiotemporal data.
method Adapting collapsed Gibbs sampling for Neyman-Scott processes via connections to mixture of finite mixture models.
result Demonstrated scalability and effectiveness on neural spike trains and document streams.
Paper investigates rigidity phenomena for weighted Ricci curvature bounds with Laplacian comparison theorem.
problem Investigating rigidity phenomena for weighted Ricci curvature bounds.
method Derived comparison geometric estimates and generalized for non-symmetric Laplacian.
result Obtained rigidity results for Laplacian comparison theorem, diameter comparisons, and volume comparisons.
We give a survey of some known results and of the many open questions in the study of generic phenomena in geometrically interesting groups.
Graph smoothing can improve learning performance by restoring lost information.
problem Graph Neural Networks (GNNs) can oversmooth, losing important information.
method Analyzing simplified linear GNNs with mean aggregation, showing benefits up to a certain point.
result Graph smoothing can restore lost information, improving both regression and classification.
Rich and complex time-series data, such as those generated from engineering systems, financial markets, videos or neural recordings, are now a common feature of modern data analysis. Explaining the phenomena underlying these diverse data sets requires flexible and accurate models. In this paper, we promote Gaussian pro…
Topological surgery is a mathematical technique used for creating new manifolds out of known ones. We observe that it occurs in natural phenomena where a sphere of dimension 0 or 1 is selected, forces are applied and the manifold in which they occur changes type. For example, 1-dimensional surgery happens during chromo…
Analyzes magnetic Laplacian on hyperbolic surfaces, highlighting key quantum phenomena.
problem Understanding quantum phenomena on hyperbolic surfaces with magnetic fields.
method Semiclassical analysis and mathematical modeling of the magnetic Laplacian.
result Discovers new insights into quantum behavior on hyperbolic surfaces with magnetic fields.