A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
New framework for attributing online marketing touchpoints.
Determinantal point process have recently been used as models in machine learning and this has raised questions regarding the characterizations of conditional independence. In this paper we investigate characterizations of conditional independence. We describe some conditional independencies through the conditions on t…
Graphical lasso may fail to fit models when data points are insufficient.
New framework models complex spatial data with basis functions and graphical vectors.
The graphics processing unit (GPU) has emerged as a powerful and cost effective processor for general performance computing. GPUs are capable of an order of magnitude more floating-point operations per second as compared to modern central processing units (CPUs), and thus provide a great deal of promise for computation…
Estimates change point in high-dimensional dynamic graphical models.
The convergence speed of stochastic gradient descent (SGD) can be improved by actively selecting mini-batches. We explore sampling schemes where similar data points are less likely to be selected in the same mini-batch. In particular, we prove that such repulsive sampling schemes lowers the variance of the gradient est…
Bayesian method estimates Kronecker graphical models from autoregressive processes.
Determinantal point processes (DPPs) are probabilistic models for repulsion. When used to represent the occurrence of random subsets of a finite base set, DPPs allow to model global negative associations in a mathematically elegant and direct way. Discrete DPPs have become popular and computationally tractable models f…
Graphical notation simplifies tensor operations and decompositions.
In this work, we explore the idea that effective generative models for point clouds under the autoencoding framework must acknowledge the relationship between a continuous surface, a discretized mesh, and a set of points sampled from the surface. This view motivates a generative model that works by progressively deform…
Paper estimates non-causal graphical models using covariance extension and transportation distance.
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…
Reciprocal processes are acausal generalizations of Markov processes introduced by Bernstein in 1932. In the literature, a significant amount of attention has been focused on developing dynamical models for reciprocal processes. In this paper, we provide a probabilistic graphical model for reciprocal processes. This le…
We characterize the sample size required for accurate graphical model selection from non-stationary samples. The observed data is modeled as a vector-valued zero-mean Gaussian random process whose samples are uncorrelated but have different covariance matrices. This model contains as special cases the standard setting …
Neural networks speed up statistical inference.
This thesis investigates belief propagation's performance in graphical models with loops.
New GPU algorithm speeds up Gaussian Process analysis.
Evaluating the log determinant of a positive definite matrix is ubiquitous in machine learning. Applications thereof range from Gaussian processes, minimum-volume ellipsoids, metric learning, kernel learning, Bayesian neural networks, Determinental Point Processes, Markov random fields to partition functions of discret…
Graphical models for covariance matrices improve structure learning.
New method reduces sample complexity for learning Ising model dynamics exponentially.
Probabilistic graphical models combine the graph theory and probability theory to give a multivariate statistical modeling. They provide a unified description of uncertainty using probability and complexity using the graphical model. Especially, graphical models provide the following several useful properties: - Graphi…
Graph neural networks extend neural Bayes estimators to irregular spatial data.
For applications as varied as Bayesian neural networks, determinantal point processes, elliptical graphical models, and kernel learning for Gaussian processes (GPs), one must compute a log determinant of an positive definite matrix, and its derivatives - leading to prohibitive computatio…
Surveying joint Gaussian graphical models to identify shared structures across domains.
Bayesian nonparametric approach for clustering non-exchangeable groups.
We propose a probabilistic formulation that enables sequential detection of multiple change points in a network setting. We present a class of sequential detection rules for certain functionals of change points (minimum among a subset), and prove their asymptotic optimality properties in terms of expected detection del…
In many structured prediction problems, complex relationships between variables are compactly defined using graphical structures. The most prevalent graphical prediction methods---probabilistic graphical models and large margin methods---have their own distinct strengths but also possess significant drawbacks. Conditio…
Bayesian method learns network structure from Gaussian process priors.
A new method combines Gaussian graphical models for better distributed Gaussian process predictions.
Reciprocal processes are acausal generalizations of Markov processes introduced by Bernstein in 1932. In the literature, a significant amount of attention has been focused on developing dynamical models for reciprocal processes. Recently, probabilistic graphical models for reciprocal processes have been provided. This …
We propose a novel graphical model selection (GMS) scheme for high-dimensional stationary time series or discrete time process. The method is based on a natural generalization of the graphical LASSO (gLASSO), introduced originally for GMS based on i.i.d. samples, and estimates the conditional independence graph (CIG) o…
Determinantal point processes (DPPs) are an important concept in random matrix theory and combinatorics. They have also recently attracted interest in the study of numerical methods for machine learning, as they offer an elegant "missing link" between independent Monte Carlo sampling and deterministic evaluation on reg…
New estimate for Curve Shortening Flow improves graphical solutions.
Efficiently estimates hub graphical models with structured sparsity.
Causal processes in biomedicine may contain cycles, evolve over time or differ between populations. However, many graphical models cannot accommodate these conditions. We propose to model causation using a mixture of directed cyclic graphs (DAGs), where the joint distribution in a population follows a DAG at any single…
The idea of computer vision as the Bayesian inverse problem to computer graphics has a long history and an appealing elegance, but it has proved difficult to directly implement. Instead, most vision tasks are approached via complex bottom-up processing pipelines. Here we show that it is possible to write short, simple …
The paper develops methods to assess and correct model uncertainties in graphical models.
Graphical models improve actuarial judgment in insurance claims analysis.
TAGM models time-varying connections between variables.
The method of covariate adjustment is often used for estimation of population average treatment effects in observational studies. Graphical rules for determining all valid covariate adjustment sets from an assumed causal graphical model are well known. Restricting attention to causal linear models, a recent article der…
Estimates log-concave densities in graphical models using tent functions.
In this paper, we introduce a new directed graphical model from Gaussian data: the Gaussian graphical interaction model (GGIM). The development of this model comes from considering stationary Gaussian processes on graphs, and leveraging the equations between the resulting steady-state covariance matrix and the Laplacia…
A method to select important experts for Gaussian processes to balance computational efficiency and uncertainty quantification.
We investigate the problem of learning discrete, undirected graphical models in a differentially private way. We show that the approach of releasing noisy sufficient statistics using the Laplace mechanism achieves a good trade-off between privacy, utility, and practicality. A naive learning algorithm that uses the nois…
This paper studies graphical model selection, i.e., the problem of estimating a graph of statistical relationships among a collection of random variables. Conventional graphical model selection algorithms are passive, i.e., they require all the measurements to have been collected before processing begins. We propose an…
The covariance structure of multivariate functional data can be highly complex, especially if the multivariate dimension is large, making extensions of statistical methods for standard multivariate data to the functional data setting challenging. For example, Gaussian graphical models have recently been extended to the…
The thesis tackles structure learning and parameter estimation for PGMs using penalized maximum likelihood methods.