We provide a classification of graphical models according to their representation as subfamilies of exponential families. Undirected graphical models with no hidden variables are linear exponential families (LEFs), directed acyclic graphical models and chain graphs with no hidden variables, including Bayesian networks …
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48 results for “hidden graphical models”
This paper extends stable blanket theory to models with hidden variables and causal cycles.
problem Identifying stable predictors in models with hidden variables and causal cycles.
method Use acyclic directed mixed graphs (ADMGs) and directed graphs (DGs) with -separation and -separation to characterize and construct intervention-stable predictor sets.
result Graphical characterizations of Markov blankets, stable frontiers, and stable blankets in models with hidden variables and cycles.
New methods for estimating causal effects in hidden variable DAGs.
problem Estimating causal effects in models with hidden variables.
method Influence function based estimators for causal effects in hidden variable DAGs.
result Achieves semiparametric efficiency bounds for identifiable effects.
Proposes a method to estimate sparse Gaussian graphical models with hidden clustering structure.
problem Modeling statistical relationships between variables with sparsity and clustering.
method Two-phase algorithm using sGS-ADMM for initial point and pALM for solution.
result Demonstrates good performance and efficiency of the proposed model and algorithm on synthetic and real data.
QT improves inference in complex PGMs with hidden variables.
problem Intractable learning and prediction errors in undirected PGMs with hidden variables.
method Query training (QT) learns a worse model to improve marginal inference.
result QT produces better marginals for a given inference algorithm than the original model.
New method learns graph structure with hidden causes from observational data.
problem Learning the structure of linear non-Gaussian models with hidden causes.
method Augments hidden variable structure by learning multidirected edges and uses higher order cumulants.
result Correct structure recovery for bow-free acyclic mixed graphs with multi-directed edges.
Pen-and-paper exercises cover various machine learning topics.
problem None explicitly stated, focuses on learning through exercises.
method Pen-and-paper exercises on machine learning topics.
result Comprehensive coverage of machine learning concepts through exercises.
Develops a new model to track financial market interconnectedness over time.
problem Investigating time-varying financial market interconnectedness.
method Hidden Markov graphical model with state-dependent generalized hyperbolic distributions.
result Identifies different degrees of network connectivity of returns over time.
Study optimal adjustment sets for causal policies with hidden variables.
problem Estimating dynamic treatment regimes with hidden variables.
method Developed criteria for graphs without hidden variables to compare estimators, extended to dynamic policies and hidden variables.
result Existence and computation of optimal minimal and globally optimal adjustment sets.
Time Adaptive Gaussian Modelstat.ML
TAGM models time-varying connections between variables.
problem Inferring temporal relationships between covariates.
method Time Adaptive Gaussian Model (TAGM) using Hidden Markov Models and Gaussian Graphical Models.
result TAGM outperforms state-of-the-art methods for temporal network inference.
Quantum graphical models (QGMs) extend the classical framework for reasoning about uncertainty by incorporating the quantum mechanical view of probability. Prior work on QGMs has focused on hidden quantum Markov models (HQMMs), which can be formulated using quantum analogues of the sum rule and Bayes rule used in class…
Quantum Graphical Models (QGMs) generalize classical graphical models by adopting the formalism for reasoning about uncertainty from quantum mechanics. Unlike classical graphical models, QGMs represent uncertainty with density matrices in complex Hilbert spaces. Hilbert space embeddings (HSEs) also generalize Bayesian …
Optimal rates for learning hidden tree structures are determined.
problem Learning hidden tree structures from noisy data.
method Study of the (noisy) information threshold and the Chow-Liu algorithm.
result Optimal rates for structure recovery are inversely proportional to the information threshold squared.
Hidden Quantum Markov Models (HQMMs) can be thought of as quantum probabilistic graphical models that can model sequential data. We extend previous work on HQMMs with three contributions: (1) we show how classical hidden Markov models (HMMs) can be simulated on a quantum circuit, (2) we reformulate HQMMs by relaxing th…
Flood extent mapping plays a crucial role in disaster management and national water forecasting. Unfortunately, traditional classification methods are often hampered by the existence of noise, obstacles and heterogeneity in spectral features as well as implicit anisotropic spatial dependency across class labels. In thi…
Graphical model has been widely used to investigate the complex dependence structure of high-dimensional data, and it is common to assume that observed data follow a homogeneous graphical model. However, observations usually come from different resources and have heterogeneous hidden commonality in real-world applicati…
In this paper we investigate the geometry of the likelihood of the unknown parameters in a simple class of Bayesian directed graphs with hidden variables. This enables us, before any numerical algorithms are employed, to obtain certain insights in the nature of the unidentifiability inherent in such models, the way pos…
Many widely studied graphical models with latent variables lead to nontrivial constraints on the distribution of the observed variables. Inspired by the Bell inequalities in quantum mechanics, we refer to any linear inequality whose violation rules out some latent variable model as a "hidden variable test" for that mod…
A graphical model is a structured representation of the data generating process. The traditional method to reason over random variables is to perform inference in this graphical model. However, in many cases the generating process is only a poor approximation of the much more complex true data generating process, leadi…
In this paper, we revisit the Kalman filter theory. After giving the intuition on a simplified financial markets example, we revisit the maths underlying it. We then show that Kalman filter can be presented in a very different fashion using graphical models. This enables us to establish the connection between Kalman fi…
We describe discrete restricted Boltzmann machines: probabilistic graphical models with bipartite interactions between visible and hidden discrete variables. Examples are binary restricted Boltzmann machines and discrete naive Bayes models. We detail the inference functions and distributed representations arising in th…
The restricted Boltzmann machine is a graphical model for binary random variables. Based on a complete bipartite graph separating hidden and observed variables, it is the binary analog to the factor analysis model. We study this graphical model from the perspectives of algebraic statistics and tropical geometry, starti…
The paper parallelizes HMM inference for efficient long-term computations.
problem Efficiently computing inference in long-term hidden Markov models.
method Parallelization using associative elements and operators for sum-product and max-product algorithms.
result The proposed parallel algorithms are computationally efficient for long time horizons.
Complex textual information extraction tasks are often posed as sequence labeling or \emph{shallow parsing}, where fields are extracted using local labels made consistent through probabilistic inference in a graphical model with constrained transitions. Recently, it has become common to locally parametrize these models…
In this paper we propose a unified framework for structured prediction with latent variables which includes hidden conditional random fields and latent structured support vector machines as special cases. We describe a local entropy approximation for this general formulation using duality, and derive an efficient messa…
We study the problem of learning a latent tree graphical model where samples are available only from a subset of variables. We propose two consistent and computationally efficient algorithms for learning minimal latent trees, that is, trees without any redundant hidden nodes. Unlike many existing methods, the observed …
Probabilistic graphical models offer a powerful framework to account for the dependence structure between variables, which is represented as a graph. However, the dependence between variables may render inference tasks intractable. In this paper we review techniques exploiting the graph structure for exact inference, b…
In many applications of finance, biology and sociology, complex systems involve entities interacting with each other. These processes have the peculiarity of evolving over time and of comprising latent factors, which influence the system without being explicitly measured. In this work we present latent variable time-va…
Machine learning provides algorithms that can learn from data and make inferences or predictions on data. Bayesian networks are a class of graphical models that allow to represent a collection of random variables and their condititional dependencies by directed acyclic graphs. In this paper, an inference algorithm for …
Hybrid framework combines PGMs and TNs for complex probabilistic modeling.
problem Combining quantum-like correlations into PGM models.
method Introducing decoherence to convert probabilistic TN models into PGMs.
result Hybrid models can represent and combine strengths of both PGMs and TNs.
Products of Hidden Markov Models(PoHMMs) are an interesting class of generative models which have received little attention since their introduction. This maybe in part due to their more computationally expensive gradient-based learning algorithm,and the intractability of computing the log likelihood of sequences under…
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…
Learning the Graphical Structure of Electronic Health Records with Graph Convolutional Transformercs.LG
Effective modeling of electronic health records (EHR) is rapidly becoming an important topic in both academia and industry. A recent study showed that using the graphical structure underlying EHR data (e.g. relationship between diagnoses and treatments) improves the performance of prediction tasks such as heart failure…
Learning with hidden variables is a central challenge in probabilistic graphical models that has important implications for many real-life problems. The classical approach is using the Expectation Maximization (EM) algorithm. This algorithm, however, can get trapped in local maxima. In this paper we explore a new appro…
A Hierarchical Graphical Model for Big Inverse Covariance Estimation with an Application to fMRIstat.ME
Brain networks has attracted the interests of many neuroscientists. From functional MRI (fMRI) data, statistical tools have been developed to recover brain networks. However, the dimensionality of whole-brain fMRI, usually in hundreds of thousands, challenges the applicability of these methods. We develop a hierarchica…
Many works have been proposed in the literature to capture the dynamics of diffusion in networks. While some of them define graphical markovian models to extract temporal relationships between node infections in networks, others consider diffusion episodes as sequences of infections via recurrent neural models. In this…
We develop a latent variable model and an efficient spectral algorithm motivated by the recent emergence of very large data sets of chromatin marks from multiple human cell types. A natural model for chromatin data in one cell type is a Hidden Markov Model (HMM); we model the relationship between multiple cell types by…
The Bitcoin transaction graph is a public data structure organized as transactions between addresses, each associated with a logical entity. In this work, we introduce a complete probabilistic model of the Bitcoin Blockchain. We first formulate a set of conditional dependencies induced by the Bitcoin protocol at the bl…
New clustering method recovers hidden tree structure from data.
problem Recovering hidden hierarchical structure in data.
method Maximum average dot product for merging clusters in hierarchical clustering.
result The algorithm produces a tree that accurately represents the underlying generative hierarchical structure.
Many real-valued stochastic time-series are locally linear (Gassian), but globally non-linear. For example, the trajectory of a human hand gesture can be viewed as a linear dynamic system driven by a nonlinear dynamic system that represents muscle actions. We present a mixed-state dynamic graphical model in which a hid…
The restricted Boltzmann machine is a network of stochastic units with undirected interactions between pairs of visible and hidden units. This model was popularized as a building block of deep learning architectures and has continued to play an important role in applied and theoretical machine learning. Restricted Bolt…
Bayesian networks with hidden variables help identify causal relationships obscured by confounding.
problem Identifying causal relationships obscured by unobserved confounders.
method Use finite -mixtures of Bayesian networks with hidden variables to recover the joint probability distribution and identify causal relationships.
result First algorithm to learn mixtures of non-empty DAGs, recovering identifiable causal relationships.
Hidden variables are ubiquitous in practical data analysis, and therefore modeling marginal densities and doing inference with the resulting models is an important problem in statistics, machine learning, and causal inference. Recently, a new type of graphical model, called the nested Markov model, was developed which …
We provide high-probability sample complexity guarantees for exact structure recovery and accurate predictive learning using noise-corrupted samples from an acyclic (tree-shaped) graphical model. The hidden variables follow a tree-structured Ising model distribution, whereas the observable variables are generated by a …
Bayesian learning in undirected graphical models|computing posterior distributions over parameters and predictive quantities is exceptionally difficult. We conjecture that for general undirected models, there are no tractable MCMC (Markov Chain Monte Carlo) schemes giving the correct equilibrium distribution over param…
New algorithm improves volatility forecasting using Pairwise Markov Chains.
problem Inability to effectively predict volatility due to feature problem and non-stationarity.
method Introduced a new algorithm for prediction with Pairwise Markov Chains (PMC), extending its capabilities.
result Enhanced performance of volatility forecasting models compared to GARCH(1,1) and feedforward neural models.
Deep belief networks are a powerful way to model complex probability distributions. However, learning the structure of a belief network, particularly one with hidden units, is difficult. The Indian buffet process has been used as a nonparametric Bayesian prior on the directed structure of a belief network with a single…
Many real-world problems encountered in several disciplines deal with the modeling of time-series containing different underlying dynamical regimes, for which probabilistic approaches are very often employed. In this paper we describe several such approaches in the common framework of graphical models. We give a unifie…