We define a family of kernels for mixed continuous/discrete hierarchical parameter spaces and show that they are positive definite.
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48 results for “mixed continuous-discrete”
This paper tackles convex-submodular minimax problems in mixed continuous-discrete domains.
problem Convex-submodular minimax problems in mixed continuous-discrete domains.
method Introduces new notions of optimality and proposes iterative algorithms combining discrete and continuous optimization.
result Characterizes convergence rates, computational complexity, and quality of solutions for convex and monotone-submodular minimax problems.
Bayesian optimization tackles mixed discrete-continuous problems with Gaussian processes.
problem Optimizing problems with both discrete and continuous variables using costly simulations.
method Relaxing discrete variables into continuous latent variables, using Bayesian optimization, and incorporating compatibility constraints with Lagrangians.
result Comparative analysis of different mixed Bayesian optimization approaches.
A new method explains mixed features for predictive models using conditional inference trees.
problem Explaining complex machine learning models with mixed features.
method Proposes a method to explain mixed features (continuous, discrete, ordinal, categorical) using conditional inference trees.
result Our method often outperforms current industry standards in various simulation studies and real-world financial data.
We propose a new framework of CatBoost that predicts the entire conditional distribution of a univariate response variable. In particular, CatBoostLSS models all moments of a parametric distribution (i.e., mean, location, scale and shape [LSS]) instead of the conditional mean only. Choosing from a wide range of continu…
Tree ensemble kernels for Bayesian optimization with known constraints over mixed-feature spacesstat.ML
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.
We propose a new framework of XGBoost that predicts the entire conditional distribution of a univariate response variable. In particular, XGBoostLSS models all moments of a parametric distribution (i.e., mean, location, scale and shape [LSS]) instead of the conditional mean only. Choosing from a wide range of continuou…
Study of filtering and smoothing in submanifolds of Euclidean space.
problem Filtering and smoothing in continuous-discrete time on submanifolds.
method Formal expressions and projection approach for prediction and smoothing.
result Agreement with classical results for prediction, differences for smoothing.
Generalized Precision Matrix for scalable estimation of nonparametric Markov networks.
problem Estimating conditional independence structure in general distributions for all data types.
method Generalized Precision Matrix (GPM) for mixed-type variables, regularized score matching framework for scalability.
result Validated theoretical results and demonstrated scalability in various settings.
NCDSSM models irregularly sampled time series with improved imputation and forecasting.
problem Accurate modeling of irregularly sampled time series with missing observations.
method Neural Continuous-Discrete State Space Model (NCDSSM) with amortized inference for auxiliary variables and flexible dynamic state parameterizations.
result Improved imputation and forecasting performance on multiple benchmark datasets.
LF-PPL: A Low-Level First Order Probabilistic Programming Language for Non-Differentiable Modelscs.LG
We develop a new Low-level, First-order Probabilistic Programming Language (LF-PPL) suited for models containing a mix of continuous, discrete, and/or piecewise-continuous variables. The key success of this language and its compilation scheme is in its ability to automatically distinguish parameters the density functio…
Paper proposes scalable method for analyzing multi-omic data.
problem Integrating high-dimensional multi-omic data for cancer subtyping.
method Mixed graphical model approach using Birth-Death MCMC algorithm.
result Our method outperforms LASSO and standard BDMCMC in computational efficiency and model selection accuracy.
This paper introduces a novel recalibration method for multivariate forecasts.
problem Multivariate calibration for potentially misspecified models.
method Local mappings between marginal probability integral transform values and observed space, using K-nearest neighbors or normalizing flows.
result Demonstrated effectiveness on currency exchange rate and childhood malnutrition data.
Graphical models provide powerful tools to uncover complicated patterns in multivariate data and are commonly used in Bayesian statistics and machine learning. In this paper, we introduce the R package BDgraph which performs Bayesian structure learning for general undirected graphical models (decomposable and non-decom…
Estimates treatment effects in randomized experiments with non-compliance.
problem Estimating distributional treatment effects in experiments with imperfect compliance.
method Proposes a regression-adjusted estimator based on distribution regression with Neyman-orthogonal moment conditions.
result Achieves semiparametric efficiency bound and demonstrates favorable performance in simulations and real data.
The paper is concerned with non-linear Gaussian filtering and smoothing in continuous-discrete state-space models, where the dynamic model is formulated as an Itô stochastic differential equation (SDE), and the measurements are obtained at discrete time instants. We propose novel Taylor moment expansion (TME) Gaussian …
On Uncertainty Estimation by Tree-based Surrogate Models in Sequential Model-based Optimizationstat.ML
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.
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 …
Learn Continuously, Act Discretely: Hybrid Action-Space Reinforcement Learning For Optimal Executionq-fin.TR
Hybrid RL method optimizes trading by balancing continuous and discrete actions.
problem Optimal execution in algorithmic trading with continuous-discrete action space.
method Combines continuous and discrete RL agents for better trading decisions.
result Significantly outperforms existing methods in trading efficiency and stability.
Stochastic domains often involve risk-averse decision makers. While recent work has focused on how to model risk in Markov decision processes using risk measures, it has not addressed the problem of solving large risk-averse formulations. In this paper, we propose and analyze a new method for solving large risk-averse …
The R package abn is designed to fit additive Bayesian models to observational datasets. It contains routines to score Bayesian networks based on Bayesian or information theoretic formulations of generalized linear models. It is equipped with exact search and greedy search algorithms to select the best network. It supp…
Hybrid continuous-discrete models naturally represent many real-world applications in robotics, finance, and environmental engineering. Inference with large-scale models is challenging because relational structures deteriorate rapidly during inference with observations. The main contribution of this paper is an efficie…
Many nonlinear extensions of the Kalman filter, e.g., the extended and the unscented Kalman filter, reduce the state densities to Gaussian densities. This approximation gives sufficient results in many cases. However, this filters only estimate states that are correlated with the observation. Therefore, sequential esti…
We introduce the thermodynamic variational objective (TVO) for learning in both continuous and discrete deep generative models. The TVO arises from a key connection between variational inference and thermodynamic integration that results in a tighter lower bound to the log marginal likelihood than the standard variatio…
New method uses continuous OT for fairness, outperforming discrete OT.
problem Fairness issues in machine learning models.
method Stochastic-gradient fairness method based on continuous optimal transport.
result Continuous OT method outperforms discrete OT when data is limited.
Deep Fair Learning: A Unified Framework for Fine-tuning Representations with Sufficient Networksstat.ML
Unified framework for fair representation learning in machine learning.
problem Ensuring fairness in machine learning models, especially when biased data representations lead to unfair predictions.
method Integrates nonlinear sufficient dimension reduction with deep learning to construct fair and informative representations, introducing a penalty term to enforce conditional independence between sensitive attributes and learned representations.
result Achieves a superior balance between fairness and utility, significantly outperforming state-of-the-art baselines on various data structures.
CGD improves diffusion models' out-of-distribution generalization.
problem Reliable sampling from high-value regions beyond training data.
method Context-guided diffusion (CGD) using unlabeled data and smoothness constraints.
result Substantial performance gains across various diffusion processes.
Decision trees are consistent for regression and classification tasks even with many predictors.
problem Consistency of decision trees with many predictors.
method CART and C4.5 methodology, oracle inequality, sparsity constraints.
result Decision trees and random forests are consistent for various types of data.
In this paper higher order mimetic discretizations are introduced which are firmly rooted in the geometry in which the variables are defined. The paper shows how basic constructs in differential geometry have a discrete counterpart in algebraic topology. Generic maps which switch between the continuous differential for…
In this paper we deal with two classes of mixed metric 3-structures, namely the mixed 3-Sasakian structures and the mixed metric 3-contact structures. Firstly we study some properties of the curvature of mixed 3-Sasakian structures, proving that any manifold endowed with such a structure is Einstein. Then we prove the …
Mixed-SCORE+ improves community detection in weak signal networks.
problem Detecting communities in weak signal networks.
method Proposes Mixed-SCORE+ combining properties of Mixed-SCORE and SCORE+.
result Significantly improves detection error rates on Polblogs and weak signal networks.
Plug-and-play L-GM-AMP improves CS recovery for any i.i.d. source prior.
problem Efficiently recovering signals from compressed measurements with unknown priors.
method Deep learning with Gaussian-mixture model to approximate source prior, combined with learned denoising.
result L-GM-AMP achieves state-of-the-art performance without prior knowledge of source distribution.
A new unbiased Hessian estimator for expectation-based objectives.
problem Estimating Hessian for objectives with non-reparameterizable nodes.
method GO Hessian estimator for expectation-based objectives.
result GO Hessian provides unbiased and low-variance estimation of Hessian.
The paper explores knotoids, pseudo knotoids, braidoids, and pseudo braidoids on the torus.
problem The study of knotoids, pseudo knotoids, braidoids, and pseudo braidoids on the torus.
method Introducing new knotoid and braidoid concepts, isotopy theorems, state sum formulas, and Alexander and Markov theorems.
result Formulation and proof of Alexander and Markov theorems for mixed knotoids and mixed pseudo knotoids.
New method for mixed memberships using symmetrized Laplacian inverse matrix.
problem Mixed memberships in community detection.
method Spectral clustering on symmetrized Laplacian inverse matrix.
result Mixed-SLIM methods outperform state-of-the-art methods.
Mixed-platonic 3-manifoldsmath.GT
New mixed-platonic 3-manifolds from different polyhedra types.
problem Finding new hyperbolic knot complements with hidden symmetries.
method Defined mixed-platonic 3-manifolds and studied their properties.
result No mixed-platonic hyperbolic knot complement has hidden symmetries.
The literature on statistical learning for time series assumes the asymptotic independence or ``mixing' of the data-generating process. These mixing assumptions are never tested, nor are there methods for estimating mixing rates from data. We give an estimator for the -mixing rate based on a single stationary sample…
Unified Minkowski problem discussed for (p,q)-mixed quermassintegrals.
problem Unified Minkowski problem for (p,q)-mixed quermassintegrals.
method Introducing (p,q)-mixed quermassintegrals and (p,q)-dual mixed curvature measure to study the Minkowski problem.
result Derivation of important properties and geometric inequalities for (p,q)-mixed quermassintegrals.
Mixed 3-structures are odd-dimensional analogues of paraquaternionic structures. They appear naturally on lightlike hypersurfaces of almost paraquaternionic hermitian manifolds. We study invariant and anti-invariant submanifolds in a manifold endowed with a mixed 3-structure and a compatible (semi-Riemannian) metric. P…
Mix-IRLS solves imbalanced mixed linear regression problems efficiently.
problem Imbalanced mixed linear regression problems.
method Sequential robust regression approach.
result Mix-IRLS outperforms other methods on imbalanced mixtures and real-world datasets.
Paper presents an econophysics model for mixed economies.
problem Understanding mixed economies in various countries.
method Developed an econophysics model with a reduced state sector participation.
result Proposed a new model with a 10-15% state sector participation.
Characterizes measures preserving compound mixed renewal process properties.
problem Preserving compound mixed renewal process properties under different probability measures.
method Characterization of progressively equivalent probability measures.
result Any compound mixed renewal process can be converted into a compound mixed Poisson process through a change of measures.
Gradient Descent Algorithm in Hilbert Spaces under Stationary Markov Chains with - and -Mixingstat.ML
Study on gradient descent in Hilbert spaces with Markov chains, focusing on mixing coefficients.
problem Analyzing convergence of gradient descent in Hilbert spaces with stationary Markov chains.
method Examined strictly stationary Markov chains with - and -mixing coefficients, derived probabilistic upper bounds.
result Probabilistic upper bounds on convergence behavior of gradient descent algorithm based on mixing coefficients.
Study on mixed Killing vector fields on Cigar Ricci-Bourguignon solitons.
problem Characterizing mixed Killing vector fields on Cigar Ricci-Bourguignon solitons.
method Analyzing the condition and using rigidity phenomena.
result Dimension of complete mixed Killing fields is 5 and a basis is explicitly determined.
Study on Kähler manifolds with non-negative mixed curvature, proving splitting and structure theorems.
problem Investigating properties of Kähler manifolds with specific curvature conditions.
method Conformal perturbation method.
result Established structure and splitting theorems for Kähler manifolds with non-negative mixed curvature.
New proof shows rapid mixing for random walks on nilmanifolds.
problem Proving rapid mixing for random walks on nilmanifolds.
method Proved rapid mixing for almost all random walks generated by m translations on nilmanifolds under mild assumptions.
result For several classical classes of nilmanifolds, m=2 suffices for rapid mixing.
We show that all non-trivial continuous endomorphisms of the circle group are topologically mixing. We also show that there exists a large infinite class of continuous endomorphisms of any n-dimensional torus group which are topologically mixing. Lastly, we prove that any continuous endomorphism on an abelian polish se…
The paper explores the relationship between joint mixability and negative dependence structures.
problem Understanding the connection between joint mixability and various negative dependence concepts.
method Analyzes the properties of joint mixes and their relation to negative dependence structures.
result Derives necessary and sufficient conditions for a joint mix to be negatively dependent.