This note provides an alternative proof of a result of Labourie. We show that the two complements of the convex core of a three dimensional quasi-fuchsian hyperbolic manifold may be foliated by embedded hypersurfaces of constant Gaussian curvature.
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Bayesian tensor train kernel machine uses Laplace approximation for scalable GP regression.
problem Scalability limitations of Gaussian process regression.
method Bayesian tensor train kernel machine with Laplace approximation and variational inference.
result VI replaces cross-validation and offers up to 65x faster training.
We first introduce a novel profile-based alignment algorithm, the multiple continuous Signal Alignment algorithm with Gaussian Process Regression profiles (SA-GPR). SA-GPR addresses the limitations of currently available signal alignment methods by adopting a hybrid of the particle smoothing and Markov-chain Monte Carl…
Tensorized Rademacher projections outperform Gaussian projections in reducing tensor dimensions.
problem Reducing the dimension of high-dimensional tensors for machine learning.
method Tensorized Rademacher random projections using Tensor Train decomposition.
result Tensorized Rademacher projections can replace Gaussian projections in tensor compression.
GPflow is a Gaussian process library that uses TensorFlow for its core computations and Python for its front end. The distinguishing features of GPflow are that it uses variational inference as the primary approximation method, provides concise code through the use of automatic differentiation, has been engineered with…
We develop a new DTSM with nonlinearities using Gaussian Processes for better interest rate forecasting.
problem Linear DTSMs fail to capture nonlinear relationships between macroeconomic variables and interest rates.
method We propose a Gaussian Process-based sequential Monte Carlo estimation and forecasting scheme.
result Nonlinear models outperform linear ones in forecasting core inflation, leading to significant economic value gains.
New GPU algorithm speeds up Gaussian Process analysis.
problem Reducing computational complexity for large spatial datasets.
method Implemented three GPU methods for Vecchia Approximation.
result New GPU method outperforms existing methods.
Gaussian process (GP) models form a core part of probabilistic machine learning. Considerable research effort has been made into attacking three issues with GP models: how to compute efficiently when the number of data is large; how to approximate the posterior when the likelihood is not Gaussian and how to estimate co…
Survey on Gaussian processes and their deep variants.
problem Limitations of Gaussian processes and their derivatives.
method Comprehensive review of existing methods and research themes.
result Advancements in Deep Gaussian Processes over the past decade.
Bayesian methods in machine learning, such as Gaussian processes, have great advantages com-pared to other techniques. In particular, they provide estimates of the uncertainty associated with a prediction. Extending the Bayesian approach to deep architectures has remained a major challenge. Recent results connected dee…
This note proves a Gaussian version of a Pólya-Szegö conjecture using rearrangement techniques.
problem Finding the domain with the minimum Gaussian principal frequency when the Gaussian torsional rigidity is fixed.
method Adapted Kohler-Jobin rearrangement technique to the Gauss space, considering a modified torsional rigidity and rearranging layers to half-spaces.
result The Gaussian principal frequency is minimized for the half-space when the Gaussian torsional rigidity is fixed.
A new method combines Gaussian Processes to optimize under uncertainty.
problem Bayesian Optimization's weakness in fitting Gaussian Processes.
method Wasserstein Barycenter Gaussian Process (WBGP) approach.
result WBGP-BO converges to the optimum, improving on vanilla BO.
New sparse Gaussian process method tackles unconstrained regression problems.
problem Dealing with physical systems that satisfy inequality constraints.
method Extends constrained Gaussian process by redefining hat basis functions.
result Reduces computational complexity from to .
In the last five years, the financial industry has been impacted by the emergence of digitalization and machine learning. In this article, we explore two methods that have undergone rapid development in recent years: Gaussian processes and Bayesian optimization. Gaussian processes can be seen as a generalization of Gau…
Simulation of the drawdown and its duration in Lévy models via stick-breaking Gaussian approximationmath.PR
Method simulates drawdown and duration in Lévy models using Gaussian approximation.
problem Simulating drawdown and duration in Lévy models with high jump activity.
method Stick-breaking Gaussian approximation for simulation, bounds on Wasserstein distances.
result Good agreement between theoretical bounds and numerical performance.
This paper establishes an equivalence between transitive double Lie algebroids and core diagrams.
problem Understanding and characterizing transitive double Lie algebroids.
method Using core diagrams and equivalence of transitive core diagrams with transitive double Lie groupoids.
result Transitive double Lie algebroids are completely determined by their core diagrams.
We study the problem of estimating the parameters of a Gaussian distribution when samples are only shown if they fall in some (unknown) subset . This core problem in truncated statistics has long history going back to Galton, Lee, Pearson and Fisher. Recent work by Daskalakis et al. (FOCS'18), provide…
Optimising black-box functions is important in many disciplines, such as tuning machine learning models, robotics, finance and mining exploration. Bayesian optimisation is a state-of-the-art technique for the global optimisation of black-box functions which are expensive to evaluate. At the core of this approach is a G…
ScaML-GP efficiently learns from few meta-tasks using Gaussian processes.
problem Exploiting historical data for quick task solving in low-data regimes.
method Modular Gaussian process model with a carefully designed multi-task kernel.
result ScaML-GP learns efficiently with few and many meta-tasks.
We derive PAC-Bayesian learning guarantees for heavy-tailed losses, and obtain a novel optimal Gibbs posterior which enjoys finite-sample excess risk bounds at logarithmic confidence. Our core technique itself makes use of PAC-Bayesian inequalities in order to derive a robust risk estimator, which by design is easy to …
Machine learning (ML) models trained by differentially private stochastic gradient descent (DP-SGD) have much lower utility than the non-private ones. To mitigate this degradation, we propose a DP Laplacian smoothing SGD (DP-LSSGD) to train ML models with differential privacy (DP) guarantees. At the core of DP-LSSGD is…
New peripheral structure for core groups detects noninvertible knots.
problem Detecting noninvertible knots and links.
method Introduced a new peripheral structure for core groups.
result The new structure detects noninvertibility of some knots and links.
In various application areas, networked data is collected by measuring interactions involving some specific set of core nodes. This results in a network dataset containing the core nodes along with a potentially much larger set of fringe nodes that all have at least one interaction with a core node. In many settings, t…
ALCORE tensor decomposition reduces computational cost for sparse count data.
problem Efficiently decompose sparse count data matrices.
method Probabilistic Tucker decomposition with -norm constraint.
result ALCORE achieves similar results to full Tucker decomposition at a fraction of the cost.
Bayesian optimization technique scaled using Vecchia approximations.
problem Scalability issue with Gaussian process surrogate models in Bayesian optimization.
method Adapted Vecchia approximation from spatial statistics to Gaussian processes, developed improvements and extensions.
result Methods compared favorably to state-of-the-art on various test functions and reinforcement learning problems.
K-means fails in high dimensions with noise and few samples.
problem Clustering in high-dimensional data with noise and limited samples.
method Simple Gaussian Mixture Model (GMM) analysis.
result Almost every partition becomes a fixed point of k-means in high dimensions.
FunBaT extends Tucker decomposition to handle continuous-indexed tensor data.
problem Handling continuous-indexed tensor data that doesn't fit traditional Tucker decomposition.
method FunBaT treats continuous-indexed data as interactions between a core tensor and a group of latent functions modeled by Gaussian processes (GP). It converts each GP into a state-space prior and uses advanced message-passing techniques for scalable inference.
result FunBaT effectively handles real-world data with continuous indexes, demonstrating its advantage in synthetic and real-world applications.
Interbank markets are often characterised in terms of a core-periphery network structure, with a highly interconnected core of banks holding the market together, and a periphery of banks connected mostly to the core but not internally. This paradigm has recently been challenged for short time scales, where interbank ma…
We introduce the notion of the visual core of a hyperbolic 3-manifold N and explore its basic properties. The visual core can be thought of as a harmonic analysis analogue of the convex core. We investigate circumstances in which the visual core of a cover N' of N embeds under the covering map from N' to N. We apply th…
Core Surfacesmath.GR
New combinatorial structures represent subgroups of surface groups, analogous to Stallings core graphs.
problem Representing subgroups of surface groups in a combinatorial way.
method Introducing core surfaces as 2-dimensional complexes made up of vertices, labeled edges, and 4g-gons.
result Core surfaces are compact when corresponding subgroups are finitely generated.
Many applications infer the structure of a probabilistic graphical model from data to elucidate the relationships between variables. But how can we train graphical models on a massive data set? In this paper, we show how to construct coresets -compressed data sets which can be used as proxy for the original data and ha…
LVM-GP solves PDEs with uncertainty using latent variables and Gaussian processes.
problem Uncertainty quantification in PDE solutions with noisy data.
method Combines latent variable model and Gaussian process for uncertainty-aware prediction.
result Efficiently captures functional dependencies and robust uncertainty quantification.
Paper introduces a core-periphery model for identifying informative network structures.
problem Noise and bias in non-informative periphery structures obscure the informative core in complex networks.
method Spectral algorithms for core identification as a preprocessing step for network analysis.
result The proposed method outperforms traditional core-periphery methods in various downstream tasks.
Gaussian processes (GPs) are important models in supervised machine learning. Training in Gaussian processes refers to selecting the covariance functions and the associated parameters in order to improve the outcome of predictions, the core of which amounts to evaluating the logarithm of the marginal likelihood (LML) o…
Kernel embeddings separate distinct probability distributions, simplifying testing.
problem Testing equality of non-atomic probability distributions.
method Kernel covariance embeddings and Gaussian measures in reproducing kernel Hilbert spaces.
result Testing for singularity between Gaussian measures is equivalent to testing for equality of non-atomic probability distributions.
New method improves GP regression by relaxing variational assumption.
problem Improving variational Gaussian processes for better predictive performance.
method Relaxing the variational assumption to a more general distribution for optimization.
result New tighter evidence lower bound for GP regression.
Entropic optimal transport beyond product reference couplings: the Gaussian case on Euclidean spacemath.ST
This work extends entropic optimal transport to non-product reference couplings, focusing on Gaussian cases.
problem Finding a diffuse coupling between two measures with non-product reference couplings.
method Reduction of the entropic optimal transport problem to a matrix optimization problem.
result Complete description of the solution for non-product reference couplings, including primal and dual variables.
Estimates covariance matrices for matrix-variate data via core covariance geometry.
problem Estimating covariance matrices for matrix-variate data with partial isotropy.
method Fixed-rank core covariance geometry, partial-isotropy rank-r core shrinkage estimator.
result The geometry of the space of rank-r cores is a smooth manifold.
Transformers solve Gaussian Mixture Models without supervision.
problem Solving Gaussian Mixture Models (GMMs) unsupervised.
method Proposes TGMM, a transformer-based framework for GMM tasks.
result Transformers can effectively solve GMM tasks, improving upon classical methods.
Probabilistic models are conceptually powerful tools for finding structure in data, but their practical effectiveness is often limited by our ability to perform inference in them. Exact inference is frequently intractable, so approximate inference is often performed using Markov chain Monte Carlo (MCMC). To achieve the…
Enhanced SMC uses gradients from CRN-PF in Langevin proposals for improved state and parameter estimation.
problem Challenges in high-dimensional parameter spaces for SMC.
method Leveraging gradients from a CRN-PF within a Langevin proposal.
result Higher effective sample size and more accurate parameter estimates.
Probabilistic programming aids in automatically dating ice cores, reducing manual error and uncertainty.
problem Automatically dating ice cores with high accuracy and capturing uncertainty.
method Probabilistic models and probabilistic programming for automatic inference.
result Demonstrated the use of probabilistic programming for ice core dating, showcasing its benefits and limitations.
Giving provable guarantees for learning neural networks is a core challenge of machine learning theory. Most prior work gives parameter recovery guarantees for one hidden layer networks, however, the networks used in practice have multiple non-linear layers. In this work, we show how we can strengthen such results to d…
Classifies stability of flat-core -elasticae pinned at boundaries.
problem Stability of flat-core -elasticae under pinned boundary conditions.
method Classification based on previous work for all and .
result Completes the classification of stable pinned -elasticae in .
A new model captures multifractal volatility in stock returns.
problem Capturing multifractal volatility in stock returns.
method Introduced mLog S-fBM model, defined mS-fBM, and developed calibration procedure.
result Validated model on synthetic and real data, showing multifractal behavior.
Identifiability Without Gaussianity: Symbolic World Models and Near-Infinite Temporal Consistencystat.ML
Symbolic grounding in causal dynamics achieves near-infinite temporal consistency.
problem Achieving linear identifiability in non-Gaussian physical systems.
method Physics-Grounded Symbolic Architecture (PGSA)
result PGSA achieves exact linear identifiability for all physical regimes.
Paper extends knowledge gradient for preferential BO, overcoming computational challenges.
problem Extending knowledge gradient to preferential BO with pairwise comparisons.
method Derive exact and analytical knowledge gradient for preferential BO.
result Exact knowledge gradient outperforms existing acquisition functions on benchmark problems.
FABLE incorporates instance features into PWS label models for improved performance.
problem Lack of instance features in existing label models limits their performance.
method FABLE uses a mixture of Bayesian label models and a Gaussian Process classifier to incorporate instance features.
result FABLE achieves the highest averaged performance across nine baselines on benchmark datasets.