Novel prior for orthogonal functions improves functional component estimation.
problem Improving orthogonality in functional principal component analysis.
method Sequential adaptive priors for orthogonal functions using hierarchical conditionally normal distributions.
result Proposed prior leads to nearly orthogonal posterior estimates.
FPCA optimizes fairness in target vectors' span.
problem Fairness in principal component analysis for multiple target vectors.
method Non-concave maximization of worst projected target norm using sub-gradient descent.
result Optimization landscape is benign with globally optimal local minima.
We found hidden convexity in FPCA and developed a faster algorithm.
problem Bias in PCA leading to unequal subgroup outcomes.
method Convex optimization via eigenvalue optimization.
result Faster and fairer PCA algorithm.
RFPCA improves robustness of FPCA for matrix data.
problem Outliers in matrix data degrade the performance of FPCA.
method RFPCA uses matrix-variate t-distribution and EM algorithm for robust estimation.
result RFPCA outperforms other methods in detecting matrix-valued outliers.
This paper aims to develop new techniques to describe joint behavior of stocks, beyond regression and correlation. For example, we want to identify the clusters of the stocks that move together. Our work is based on applying Kernel Principal Component Analysis(KPCA) and Functional Principal Component Analysis(FPCA) to …
A method for noise reduction in functional time series using FPCA.
problem Noise contamination in functional time series.
method Extending FPCA to separate signal and noise components.
result Optimal projection minimizes mean integrated squared error.
We consider the sampling problem for functional PCA (fPCA), where the simplest example is the case of taking time samples of the underlying functional components. More generally, we model the sampling operation as a continuous linear map from H to Rm, where the functional components to lie in so…
Proposes FunNoL for better curve classification and reconstruction in multivariate functional data.
problem Linear methods fail to capture nonlinear structures in multivariate functional data.
method Functional nonlinear learning (FunNoL) method using nonlinear mapping.
result FunNoL outperforms FPCA in curve classification and reconstruction, especially in multivariate settings.
A new method clusters rows of a matrix of point processes.
problem Challenges in analyzing structured point process data.
method Mixture model of multi-level marked point processes, combined with ES algorithm and FPCA.
result An efficient method for clustering rows of a matrix of point processes.
Study on liquidity dynamics in Uniswap v3 pools using statistical methods.
problem Characterize liquidity in Uniswap v3 pools.
method Functional principal component analysis (FPCA) and dynamic factor methods.
result Liquidity dynamics in Uniswap v3 pools are well-captured by a low-order Legendre polynomial basis.
The paper proposes a new method for clustering survival data using smoothed log-hazard trajectories.
problem Clustering survival data based on instantaneous risk dynamics.
method Functional Principal Component Analysis applied to B-spline smoothed log-hazard trajectories.
result The proposed method provides an interpretable representation of relative temporal risk dynamics.
A new PCA method for analyzing point processes.
problem Analyzing variability in replicated point processes.
method Functional Principal Component Analysis (fPCA) on cumulative mass functions.
result Established convergence and introduced principal measures.
Enhances Random Forest for imbalanced functional data classification.
problem Challenges in classifying imbalanced functional data.
method Functional Random Forest with Adaptive Cost-Sensitive Splitting (FRF-ACS).
result Significantly improves minority class recall and predictive performance.
New algorithm solves fair PCA, robust PCA, and sparse PCA problems efficiently.
problem Fair Principal Component Analysis (FPCA) to ensure fairness in PCA solutions.
method Iterative MM algorithm with SDP reformulation to quadratic program.
result Algorithm monotonically improves fairness objectives at each iteration.
The paper presents a method to reduce arm motion complexity for prosthetics and robotics.
problem Reducing the complexity of human arm motions for robotic and prosthetic control.
method Data-driven techniques including DTW, DBA, Ward's distance, batch-DTW, and fPCA.
result Representative motion clusters and averages for different arm DOF levels.
Unified Bayesian-AI framework improves epidemiological risk prediction and uncertainty quantification.
problem Lack of calibrated uncertainty in machine learning models for epidemiology.
method Combines Bayesian prediction with Bayesian hyperparameter optimization using logistic regression and Gaussian-process Bayesian optimization.
result Unified Bayesian-AI framework provides reliable coverage and improved calibration, enhancing epidemiological decision making.
We exhibit a strong link between frequentist PAC-Bayesian risk bounds and the Bayesian marginal likelihood. That is, for the negative log-likelihood loss function, we show that the minimization of PAC-Bayesian generalization risk bounds maximizes the Bayesian marginal likelihood. This provides an alternative explanatio…
PAC-Bayesian bounds for MLPs with cross entropy loss validated.
problem Generalization bounds for MLPs with cross entropy loss.
method Introduced probabilistic explanations and proved PAC-Bayesian bounds using ELBO.
result MLPs with cross entropy loss inherently guarantee PAC-Bayesian generalization bounds.
Review of priors in Bayesian deep learning models.
problem The importance of prior choices in Bayesian deep learning models.
method Overview of different priors and methods of learning priors from data.
result Motivate practitioners to think carefully about prior specification.
Bayesian methods enhance deep learning models by improving reliability and uncertainty.
problem Improving reliability and uncertainty awareness in deep learning models.
method Approximate Bayesian inference techniques, including SG-MCMC and VI, applied to deep learning models.
result Enhanced posterior inference for deep learning models, particularly in neural networks and generative models.
Enhances robustness in experimental design through Generalised Bayesian inference.
problem Poor inference and estimates of information gain when statistical model is incorrectly specified.
method Generalised Bayesian (Gibbs) inference framework applied to experimental design.
result GBOED enhances robustness to outliers and incorrect assumptions about noise distribution.
Bayesian neural networks speed up numerical integration.
problem Scalability of Bayesian quadrature methods.
method Bayesian Stein networks using neural networks and Laplace approximation.
result Orders of magnitude speed-up on benchmark functions and real-world problems.
Bayesian uncertainty quantification is flawed, according to new research.
problem Flawed interpretation of Bayesian uncertainty quantification.
method Discussion of Bayesian updating and optimization-based perspective, proposing measures of quality.
result Bayesian uncertainty quantification is not coherent with optimization-based perspective.
Bayesian MAML outperforms MAML in meta learning tasks with theoretical guarantees.
problem Theoretical understanding of Bayesian MAML's superiority over MAML.
method Comparison of meta test risks between Bayesian MAML and MAML in meta linear regression.
result Bayesian MAML has provably lower meta test risks than MAML in both distribution agnostic and linear centroid cases.
One of the main challenges of deep learning tools is their inability to capture model uncertainty. While Bayesian deep learning can be used to tackle the problem, Bayesian neural networks often require more time and computational power to train than deterministic networks. Our work explores whether fully Bayesian netwo…
Bayesian REX learns Atari games from demonstrations efficiently.
problem Bayesian reward learning for complex control problems is computationally intractable.
method Bayesian Reward Extrapolation (Bayesian REX) pre-trains a low-dimensional feature encoding and uses preferences to perform fast Bayesian inference.
result Bayesian REX learns Atari games from demonstrations in 5 minutes, competitive with state-of-the-art methods.
Bayesian coresets improve scalable Bayesian inference.
problem Efficiently approximating posterior inference with a subset of data.
method Sparsity constrained optimization and accelerated optimization methods.
result Explicit convergence rate guarantees and superior performance compared to state-of-the-art.
Nonlinear MCMC improves Bayesian machine learning sampling.
problem Sampling problems in Bayesian machine learning.
method Nonlinear MCMC technique with convergence guarantees.
result Improves sampling in Bayesian neural networks.
Discussing hybrid models in Bayesian networks.
problem Improving accuracy in network modeling.
method Hybrid semiparametric Bayesian approach.
result Enhanced model performance in complex networks.
FP-BMA improves generalization by encouraging flat posteriors in Bayesian Model Averaging.
problem Lack of flat posterior in approximate Bayesian inference methods hinders effective Bayesian Model Averaging.
method Proposes Flat Posterior-aware Bayesian Model Averaging (FP-BMA) and Flat Posterior-aware Bayesian Transfer Learning schemes.
result FP-BMA successfully captures flat posteriors, improving generalization performance.
Proposes OBS, a method to adaptively combine Bayesian models online.
problem Learning optimal combinations of Bayesian models in online learning.
method Empirical Bayes lens, Online Bayesian Stacking (OBS).
result Establishes a novel connection between OBS and portfolio selection.
We study the problem of learning Bayesian network structures from data. We develop an algorithm for finding the k-best Bayesian network structures. We propose to compute the posterior probabilities of hypotheses of interest by Bayesian model averaging over the k-best Bayesian networks. We present empirical results on s…
Bayesian neural networks use temperature adjustments to improve predictive performance.
problem Lack of theoretical generalization guarantees for Bayesian neural networks.
method Temperature adjustments to balance likelihood and prior regularization.
result Improved predictive performance through temperature adjustments.
SCoreBO improves Bayesian optimization by learning hyperparameters and self-correcting.
problem Efficient hyperparameter tuning for Gaussian process models in Bayesian optimization.
method Introduces SAL and SCoreBO, which prioritize hyperparameter learning and perform simultaneous optimization and learning.
result SCoreBO outperforms state-of-the-art methods on traditional benchmarks and atypical tasks.
In this paper we introduce ZhuSuan, a python probabilistic programming library for Bayesian deep learning, which conjoins the complimentary advantages of Bayesian methods and deep learning. ZhuSuan is built upon Tensorflow. Unlike existing deep learning libraries, which are mainly designed for deterministic neural netw…
Bayesian optimization with cost-awareness using Gittins index.
problem Optimizing unknown functions with limited data evaluations and costs.
method Developed a connection between cost-aware Bayesian optimization and the Pandora's Box problem, using the Gittins index as an acquisition function.
result The Gittins index-based acquisition function performs well in cost-aware Bayesian optimization, especially in high dimensions.
This work improves mixing rates for Bayesian CART, a key component of BART.
problem Understanding and improving mixing rates for Bayesian inference with MCMC.
method Derived upper bounds on mixing times, provided sufficient conditions for polynomial mixing, and proposed Twiggy Bayesian CART.
result Twiggy Bayesian CART achieves polynomial mixing without assuming signal connectivity.
Bayesian hybrid models fuse physics-based insights with machine learning constructs to correct for systematic bias. In this paper, we compare Bayesian hybrid models against physics-based glass-box and Gaussian process black-box surrogate models. We consider ballistic firing as an illustrative case study for a Bayesian …
Inference in popular nonparametric Bayesian models typically relies on sampling or other approximations. This paper presents a general methodology for constructing novel tractable nonparametric Bayesian methods by applying the kernel trick to inference in a parametric Bayesian model. For example, Gaussian process regre…
Novel framework for Bayesian reinforcement learning infers value function distributions.
problem Bayesian reinforcement learning's challenges in inferring value function distributions.
method Inferential Induction framework for Bayesian reinforcement learning, developing Bayesian Backwards Induction algorithm.
result Proposed algorithm is competitive with state-of-the-art methods.
Bayesian networks with latent variables are characterized and their likelihoods compared.
problem Characterizing and comparing likelihoods of Bayesian networks with latent variables.
method Characterized likelihood function and empirical Bayesian network. Proved dominance of global maximum likelihood from empirical model.
result The global maximum likelihood of the original Bayesian network is attained if and only if parameters are consistent with empirical model.
Explosive growth in data and availability of cheap computing resources have sparked increasing interest in Big learning, an emerging subfield that studies scalable machine learning algorithms, systems, and applications with Big Data. Bayesian methods represent one important class of statistic methods for machine learni…
We focus on an interpolation method referred to Bayesian reconstruction in this paper. Whereas in standard interpolation methods missing data are interpolated deterministically, in Bayesian reconstruction, missing data are interpolated probabilistically using a Bayesian treatment. In this paper, we address the framewor…
Recently several researchers have investigated techniques for using data to learn Bayesian networks containing compact representations for the conditional probability distributions (CPDs) stored at each node. The majority of this work has concentrated on using decision-tree representations for the CPDs. In addition, re…
Study improves Bayesian optimisation with ensemble transfer learning.
problem Improving sample efficiency in Bayesian optimisation of expensive functions.
method Empirical analysis of ensemble-based transfer learning methods and pipeline components.
result Two components (warm start initialisation and positive weight constraint) improve transfer learning Bayesian optimisation performance.
Bayesian priors offer a compact yet general means of incorporating domain knowledge into many learning tasks. The correctness of the Bayesian analysis and inference, however, largely depends on accuracy and correctness of these priors. PAC-Bayesian methods overcome this problem by providing bounds that hold regardless …
A new clustering method using Bayesian techniques improves robustness and interpretability.
problem Improving clustering techniques for better robustness and interpretability.
method The paper proposes a novel Bayesian clustering method using the proper Bayesian bootstrap, which combines k-means clustering and ensemble clustering.
result The method provides clear indication on the optimal number of clusters and a better representation of the clustered data.
Bayesian networks are typically faithful, with implications for causal inference.
problem Determining the typicality of faithfulness in Bayesian networks.
method Analysis of Bayesian networks over a given DAG, parametrized by conditional exponential families, and nonparametric conditional densities.
result The faithful Bayesian networks are dense and open with respect to the total variation metric, extending existing results for specific classes of Bayesian networks.