SetRank tackles collaborative ranking from implicit feedback using setwise Bayesian approach.
problem Challenges in pairwise and listwise approaches for implicit feedback.
method SetRank is a novel setwise Bayesian approach that accommodates implicit feedback characteristics.
result SetRank outperforms state-of-the-art baselines on real-world datasets.
In this paper we propose an approach to preference elicitation that is suitable to large configuration spaces beyond the reach of existing state-of-the-art approaches. Our setwise max-margin method can be viewed as a generalization of max-margin learning to sets, and can produce a set of "diverse" items that can be use…
It is shown that for any locally knotted edge of a 3-connected graph in S3, there is a ball that contains all of the local knots of that edge and is unique up to an isotopy setwise fixing the graph. This result is applied to the study of topological symmetry groups of graphs embedded in S3.
A hyperelliptic broken Lefschetz fibration is a generalization of a hyperelliptic Lefschetz fibration. We construct and compute a local signature of hyperelliptic directed broken Lefschetz fibrations by generalizing Endo's local signature of hyperelliptic Lefschetz fibrations. It is described by his local signature and…
It is known that the space of convex polygons in the Euclidean plane with fixed normals, up to homotheties and translations, endowed with the area form, is isometric to a hyperbolic polyhedron. In this note we show a class of convex polygons in the Lorentzian plane such that their moduli space, if the normals are fixed…
An automorphism α of a group G is normal if it fixes every normal subgroup of G setwise. We give an algebraic description of normal automorphisms of relatively hyperbolic groups. In particular, we prove that for any relatively hyperbolic group G, Inn(G) has finite index in the subgroup Autn(G) of normal au…
Study Goeritz groups of link decompositions, focusing on their asymptotic behavior.
problem Understanding the asymptotic behavior of Goeritz groups for link decompositions.
method Defined Goeritz groups for link decompositions, analyzed their properties, and discussed their asymptotic behavior.
result Discussed the asymptotic behavior of minimal pseudo-Anosov entropies and related it to Goeritz groups of Heegaard splittings.
This paper extends braid lifting to coloured braid groupoids for all simple disc covers.
problem Lifting braids to homeomorphisms on branched covers of the disc.
method Defines a map from a coloured braid groupoid to a mapping class groupoid for all simple covers of the disc.
result Characterizes the lift of every coloured braid, recovering classical lifting on liftable braids.
Authors prove a conjecture about the Goeritz group of 3-sphere Heegaard splittings.
problem The Goeritz group of a genus g Heegaard splitting of the 3-sphere.
method Proof relies on the topological minimality of Heegaard surfaces and their disk complexes.
result The Goeritz group is generated by four specific elements for g ≥ 3.
Establishes a rank inequality between knot Floer homologies of freely 2-periodic knots and their quotients.
problem Knot Floer homology of freely 2-periodic knots and their quotients
method Large's generalization of Seidel-Smith's localization spectral sequence
result Rank inequality between knot Floer homologies
Consider the unit ball, B=D×[0,1], containing n unknotted arcs a1,a2,...,an such that the boundary of each ai lies in D×{0}. The Hilden (or Wicket) group is the mapping class group of B fixing the arcs a1∪a2∪...∪an setwise and fixing D×{1} pointwise. T…
There are several Teichmüller spaces associated to a surface of infinite topological type, after the choice of a particular basepoint (a complex or a hyperbolic structure on the surface). These spaces include the quasiconformal Teichmüller space, the length spectrum Teichmüller space, the Fenchel-Nielsen Teichmüller sp…
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…
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.
Bayesian neural networks (BNNs) augment deep networks with uncertainty quantification by Bayesian treatment of the network weights. However, such models face the challenge of Bayesian inference in a high-dimensional and usually over-parameterized space. This paper investigates a new line of Bayesian deep learning by pe…
Bayesian quadrature uses probabilistic models for estimating intractable integrals.
problem Estimating intractable integrals in complex models.
method Probabilistic, model-based approach using Gaussian processes.
result Comprehensive review and systematic taxonomy of Bayesian quadrature methods.
Semiparametric Bayesian networks combine parametric and nonparametric models for flexible data analysis.
problem Combining the advantages of parametric and nonparametric models for flexible data analysis.
method Semiparametric Bayesian networks combining parametric and nonparametric conditional probability distributions. Modifications of two algorithms for structure learning from data.
result Accurately learns the combination of parametric and nonparametric components, comparable to state-of-the-art methods.
Bayesian Markowitz portfolio problem shows entropy regularization is ineffective.
problem Entropy regularization in Bayesian Markowitz portfolio optimization.
method Combines continuous-time Bayesian filtering with stochastic policy optimization.
result Entropy regularization does not accelerate learning of unknown drift.