GP-BART improves BART's predictive performance by incorporating Gaussian process priors.
problem Lack of smoothness and explicit covariance structure in BART.
method GP-BART extends BART with Gaussian process priors for tree predictions.
result GP-BART outperforms traditional models in various applications.
Researchers improve tree model recovery from noisy data.
problem Learning tree structured models from corrupted data.
method Linear latent tree models and continuous corruption model.
result Chow-Liu algorithm consistently learns tree from noisy data.
A new tree model, GRST, improves option pricing without log-normality assumptions.
problem Limitations of CRR binomial trees in valuing securities with early exercise characteristics.
method Gaussian Recombining Split Tree (GRST) that generates a discrete probability mass function approximating a Gaussian distribution.
result Option prices from GRST align closely with market prices.
EM algorithm converges to global max in latent Gaussian tree models.
problem Optimizing log-likelihood in latent Gaussian tree models.
method Analyzed the optimization landscape and convergence of EM algorithm.
result EM algorithm converges to global maximum in latent Gaussian tree models.
Efficiently learns Gaussian tree models with near-optimal sample complexity.
problem Learning tree-structured Gaussian distributions efficiently.
method Conditional mutual information tester for Gaussian variables, near-optimal sample complexity.
result Near-optimal sample complexity for structure learning of Gaussian tree models.
The problem of learning tree-structured Gaussian graphical models from independent and identically distributed (i.i.d.) samples is considered. The influence of the tree structure and the parameters of the Gaussian distribution on the learning rate as the number of samples increases is discussed. Specifically, the error…
This study converts BART to Gaussian process regression, revealing its limitations and potential improvements.
problem Understanding the Gaussian process limit of BART and its implications.
method Deriving and computing BART's prior covariance function, implementing the infinite trees limit as GP regression, and tuning hyperparameters.
result The Gaussian process limit of BART is inferior to standard BART but can be made competitive with proper hyperparameter tuning.
BARK optimizes black-box functions using Bayesian Additive Regression Trees.
problem Bayesian optimization of complex, black-box functions with uncertainty quantification.
method BART Kernel using tree agreement for posterior over piecewise-constant functions, explored using MCMC.
result BARK obtains samples of Gaussian processes for function distributions, enabling acquisition functions for optimization.
We introduce block-tree graphs as a framework for deriving efficient algorithms on graphical models. We define block-tree graphs as a tree-structured graph where each node is a cluster of nodes such that the clusters in the graph are disjoint. This differs from junction-trees, where two clusters connected by an edge al…
Paper proposes a VB method for TS-SBP mixture models with reduced computational cost.
problem Efficiently learning tree-structured stick-breaking process mixture models.
method Utilizes Bayes coding algorithm for context tree models to calculate sums over all possible trees.
result Proposes a learning algorithm with less computational cost for TS-SBP mixture of Gaussians.
The benefits of diversifying risks are difficult to estimate quantitatively because of the uncertainties in the dependence structure between the risks. Also, the modelling of multidimensional dependencies is a non-trivial task. This paper focuses on one such technique for portfolio aggregation, namely the aggregation o…
Optimal algorithms learn Gaussian trees and polytrees from data.
problem Learning undirected Gaussian trees and polytrees from data.
method Two approaches: Chow-Liu algorithm for tree structure and modified PC algorithm for polytree structure.
result Explicit finite-sample guarantees and matching lower bounds for both approaches.
We present an integrated approach for structure and parameter estimation in latent tree graphical models. Our overall approach follows a "divide-and-conquer" strategy that learns models over small groups of variables and iteratively merges onto a global solution. The structure learning involves combinatorial operations…
Gaussian latent tree models, or more generally, Gaussian latent forest models have Fisher-information matrices that become singular along interesting submodels, namely, models that correspond to subforests. For these singularities, we compute the real log-canonical thresholds (also known as stochastic complexities or l…
New MC-Tree method combines Monte Carlo and binomial tree for option pricing and CVA.
problem Combining Monte Carlo and binomial tree methods for accurate and efficient option pricing and CVA calculations.
method MC-Tree method that mixes Monte Carlo and binomial tree parameters, using maximum entropy distributions for compound densities.
result MC-Tree method provides accurate and efficient option pricing and CVA calculations.
This work considers the problem of learning the structure of multivariate linear tree models, which include a variety of directed tree graphical models with continuous, discrete, and mixed latent variables such as linear-Gaussian models, hidden Markov models, Gaussian mixture models, and Markov evolutionary trees. The …
We describe various sets of conditional independence relationships, sufficient for qualitatively comparing non-vanishing squared partial correlations of a Gaussian random vector. These sufficient conditions are satisfied by several graphical Markov models. Rules for comparing degree of association among the vertices of…
New method improves stability of Gaussian process approximations.
problem Numerical instability in Gaussian process computations.
method Cover tree modification for inducing points, alternative sparse approximation.
result Improved stability and predictive performance in spatial tasks.
Tree structured graphical models are powerful at expressing long range or hierarchical dependency among many variables, and have been widely applied in different areas of computer science and statistics. However, existing methods for parameter estimation, inference, and structure learning mainly rely on the Gaussian or…
In this paper, we present a general, multistage framework for graphical model approximation using a cascade of models such as trees. In particular, we look at the problem of covariance matrix approximation for Gaussian distributions as linear transformations of tree models. This is a new way to decompose the covariance…
A hybrid model for Bayesian optimization handles mixed variables using MCTS for categorical and GP for continuous.
problem Optimizing functions with mixed variable types (continuous, integer, categorical).
method Merges MCTS for categorical and GP for continuous variables, integrates UCTS search strategy, and dynamically selects kernels.
result Hybrid models outperform traditional methods in Bayesian optimization.
Consider jointly Gaussian random variables whose conditional independence structure is specified by a graphical model. If we observe realizations of the variables, we can compute the covariance matrix, and it is well known that the support of the inverse covariance matrix corresponds to the edges of the graphical model…
This paper proposes an online tree-based Bayesian approach for reinforcement learning. For inference, we employ a generalised context tree model. This defines a distribution on multivariate Gaussian piecewise-linear models, which can be updated in closed form. The tree structure itself is constructed using the cover tr…
Robustifies tree learning algorithms for corrupted data.
problem Learning latent tree structures with corrupted vector observations.
method Presented robustified algorithms using truncated inner product.
result Optimalities of robust CLRG and NJ verified by sample complexities and impossibility results.
Tree ensemble kernels improve Bayesian optimization for mixed features and constraints.
problem Optimizing over mixed-feature spaces with known constraints.
method Kernel interpretation of tree ensembles as Gaussian Process prior, compatible optimization formulation for acquisition function, integration of known constraints.
result Framework outperforms state-of-the-art methods for mixed-feature spaces and constraints.
A novel stepwise VI method using vine copulas for complex latent dependence.
problem Modeling complex latent dependence structures in probabilistic models.
method Stepwise estimation of vine copula parameters using Rényi divergence and a stopping criterion.
result Our method outperforms mean-field VI and is more parsimonious in complex applications.
Dynamic Vine Copulas detect and quantify time-varying higher-order interactions in multivariate systems.
problem Time-varying dependence in multivariate systems, including tail behavior, asymmetry, and conditional structure.
method Dynamic Vine Copulas (DVC) framework for estimating and diagnosing non-Gaussian dependence, using fixed-root-order C-vines and smooth parameter trajectories.
result DVC detects and quantifies time-varying higher-order interactions, distinguishing between pairwise and conditional dependence.
Bayesian methods improve drug discovery experiment design.
problem Optimizing drug screening experiments in high-dimensional data.
method Bayesian inference and optimisation with upper confidence bound algorithms, Thompson sampling, and sparse tree search.
result Sparse tree search techniques outperform other methods in drug toxicity screening.
Combines BART and Gaussian process for spatial covariate prediction with uncertainty.
problem Improving spatial prediction models with nonlinear and interaction covariates.
method Bayesian Additive Regression Trees (BART) combined with Gaussian process for spatial dependence.
result Effective in reducing computational burden through INLA and MCMC.
A new tree-based model improves uncertainty estimation in sequential optimization.
problem Improving uncertainty estimation in sequential model-based optimization.
method Proposed a new ensemble of randomized trees (BwO forest) with bagging and oversampling.
result BwO forest outperforms existing tree-based models in various optimization scenarios.
In latent Gaussian trees the pairwise correlation signs between the variables are intrinsically unrecoverable. Such information is vital since it completely determines the direction in which two variables are associated. In this work, we resort to information theoretical approaches to achieve two fundamental goals: Fir…
In this paper, learning of tree-structured Gaussian graphical models from distributed data is addressed. In our model, samples are stored in a set of distributed machines where each machine has access to only a subset of features. A central machine is then responsible for learning the structure based on received messag…
Regression trees learn gradients of differentiable functions.
problem Understanding gradients of differentiable functions using regression trees.
method Developed a method to estimate gradients of differentiable functions using regression trees and exposed quantities from tree learning libraries.
result Gradient estimates from regression trees can be used to improve predictive analysis and solve tasks in uncertainty quantification.
CAT method learns causal structure of directed trees efficiently.
problem Learning causal structure from directed trees.
method Chu-Liu-Edmonds algorithm for fast and scalable structure learning.
result Consistency in asymptotic regime with vanishing identifiability gap for Gaussian errors.
New algorithm recovers graph structure from noisy data.
problem Noise corrupts structure in Gaussian graphical models, making identification impossible.
method Developed an algorithm to recover graph structure up to an unavoidable ambiguity.
result Algorithm recovers graph structure up to an identified ambiguity, revealing local clustering and connectivity.
Fairness, through its many forms and definitions, has become an important issue facing the machine learning community. In this work, we consider how to incorporate group fairness constraints in kernel regression methods, applicable to Gaussian processes, support vector machines, neural network regression and decision t…
Improved algorithm for partial recovery of tree-structured graphs with noisy data.
problem Learning Ising tree models with noisy observations.
method Symmetrized Geometric Averaging (SGA) algorithm with improved sample complexity.
result Significantly better sample complexity for partial tree recovery.
Sum-Product Networks (SPNs) can be regarded as a form of deep graphical models that compactly represent deeply factored and mixed distributions. An SPN is a rooted directed acyclic graph (DAG) consisting of a set of leaves (corresponding to base distributions), a set of sum nodes (which represent mixtures of their chil…
Bayesian learning for forests and trees improves graph detection and structure learning.
problem Learning graph structures in non-decomposable graphs.
method Adapted MCMC and SSS algorithms for forests and trees, using the Chow-Liu algorithm and Matrix Tree Theorem.
result SSS with trees or forests outperforms SSS with decomposable graphs in certain cases.
SMAC method optimizes tree-boosting hyperparameters best.
problem Optimizing hyperparameters for tree-boosting to improve model accuracy.
method Compared and evaluated various hyperparameter optimization methods.
result SMAC method outperforms other methods for hyperparameter tuning.
Combines boosting and latent Gaussian models for better predictions.
problem Boosting's assumptions and latent Gaussian models' limitations.
method Integrates tree-boosting and latent Gaussian models.
result Increased prediction accuracy in simulations and real-world data.
We consider the problem of the estimation of a high-dimensional probability distribution from i.i.d. samples of the distribution using model classes of functions in tree-based tensor formats, a particular case of tensor networks associated with a dimension partition tree. The distribution is assumed to admit a density …
DistGP models multi-robot mapping with distributed Gaussian process learning.
problem Collaborative mapping by multiple robots with limited local data.
method Sparse Gaussian process with factorisation and distributed training via GBP.
result DistGP achieves superior accuracy and robustness compared to DiNNO.
Study non-asymptotic estimation bounds for LTI models with Gaussian noise.
problem Estimating parameters of LTI models with non-asymptotic error bounds.
method Sharp non-asymptotic lower bounds using Cramér-Rao and van Trees inequalities, concentration results, and differential geometric constructions.
result Sharp and rate-optimal lower bounds for mean square estimation risk.
A new algorithm, Regular Tree Search, tackles non-convex simulation optimization problems.
problem Non-convex objective functions in simulation optimization.
method Integrates adaptive sampling with recursive partitioning of the search space.
result Proves global convergence and reliably identifies the global optimum.
New algorithms learn polytree structures from data.
problem Learning causal graphs from non-Gaussian data.
method Combines Chow-Liu algorithm with edge orientation schemes.
result Established high-dimensional consistency results.
A censored transformed model for proportional outcomes with boundary mass and an application to loss given default modeling.
problem Modeling proportional outcomes with boundary mass in loss given default (LGD) modeling.
method Zero-one censored transformed normal (ZOC-TN) model.
result Captures a wider range of qualitative density shapes than benchmark models while being parsimonious, computationally efficient, and numerically stable.
Algorithm recovers permutations of high-dimensional Gaussian vectors with constant correlation.
problem Recovering permutations of high-dimensional Gaussian vectors with constant correlation.
method Computing and comparing weighted counts of specially chosen wide trees.
result Polynomial-time algorithm for exact recovery at constant correlation.