We introduce an approximate search algorithm for fast maximum a posteriori probability estimation in probabilistic programs, which we call Bayesian ascent Monte Carlo (BaMC). Probabilistic programs represent probabilistic models with varying number of mutually dependent finite, countable, and continuous random variable…
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48 results for “probabilistic mappings”
PRISM provides real-time SLAM with uncertainty estimates for agent and map states.
problem Lack of uncertainty estimates and real-time capability in SLAM.
method Combines differentiable rendering and 6-DoF dynamics, uses approximations for Bayesian inference.
result Runs at 10Hz real-time with similar accuracy to state-of-the-art SLAM.
Enhanced probabilistic sampling on manifolds using Double Diffusion Maps and Geometric Harmonics.
problem Overfitting and loss of generalization in PLoM when N is small and dimensionality approaches N.
method Extending PLoM with Double Diffusion Maps and Geometric Harmonics to handle small N and high-dimensional data.
result Effective and robust method for generating statistically consistent realizations from limited data.
DPSOM combines self-organizing maps with deep learning for better data clustering.
problem Improving clustering performance in complex data.
method Integrates self-organizing maps with probabilistic clustering using a VAE.
result DPSOM outperforms current deep clustering methods in various applications.
Increasing availability of vehicle GPS data has created potentially transformative opportunities for traffic management, route planning and other location-based services. Critical to the utility of the data is their accuracy. Map-matching is the process of improving the accuracy by aligning GPS data with the road netwo…
The paper explores how to learn models that respect constraints in probabilistic learning.
problem Learning models that respect declared constraints in probabilistic learning.
method Mathematical inquiry on tractable probabilistic models like sum-product networks.
result Determines conditions under which constraints can be integrated with model learning.
We introduce the Locally Linear Latent Variable Model (LL-LVM), a probabilistic model for non-linear manifold discovery that describes a joint distribution over observations, their manifold coordinates and locally linear maps conditioned on a set of neighbourhood relationships. The model allows straightforward variatio…
New CNN approach reduces overconfidence in object classification predictions.
problem Overconfident predictions from deep models, especially SoftMax layer.
method Introduces CNN probabilistic approach using Logit layer for Bayesian inference.
result Proposed approach shows promising performance compared to SoftMax.
CMDNet simplifies MAP detection for large systems with probabilistic relaxation.
problem High complexity of MAP detection in large systems.
method Probabilistic Continuous relaxation of discrete variables, iterative CMD algorithm, CMDNet with online optimization.
result CMDNet achieves a promising accuracy-complexity trade-off in MIMO systems.
This paper introduces a neural operator for probabilistic conditioning.
problem Probabilistic conditioning of random variables given .
method Develops a single operator that maps any joint density to its conditional, approximated by neural operators.
result Neural operators can approximate the conditioning operator to arbitrary accuracy.
GPMI method interpolates uncertain atrial conduction velocity on non-Euclidean manifolds.
problem Uncertainty in atrial conduction velocity calculations.
method Gaussian Process Manifold Interpolation (GPMI) on human atrial manifolds.
result GPMI accounts for atrial topology and calculates CV uncertainty.
We introduce a toy probabilistic model to analyze job-matching processes in recent Japanese labor markets for university graduates by means of statistical physics. We show that the aggregation probability of each company is rewritten by means of non-linear map under several conditions. Mathematical treatment of the map…
Agent learns to navigate uncertain 3D maps using a hybrid planner.
problem Planning in 3D environments with uncertain topological maps.
method Hierarchical strategy combining graph planner and local policy, data-driven learning with neural network.
result Machine learning can overcome missing information in probabilistic topological maps.
This work links SOMs and GMMs, providing a mathematical basis for their use.
problem Understanding the relationship between SOMs and GMMs.
method Mathematical treatment showing SOMs as gradient descent on a GMM log-likelihood.
result SOMs can be interpreted as probabilistic models, justifying their use in various applications.
Unified tractability conditions for various compositional inference queries.
problem Analyzing tractability of probabilistic and causal inference queries.
method Algebraic perspective on circuits, focusing on semiring operators.
result Unified sufficient conditions for tractable composition of operators.
A new probabilistic framework for optimal transport using collective graphical models.
problem Measuring similarity between probability distributions and histograms.
method Probabilistic Optimal Transport based on Collective Graphical Models.
result OT with entropic regularization is equivalent to maximizing a posterior probability of a CGM.
LDF combines neural networks with probabilistic models for data fusion.
problem Combining limited primary data with readily available auxiliary data.
method Neural networks as conjugate mappings of auxiliary data for posterior analysis.
result Efficient inference and compact latent variable posterior distributions.
A deep learning method for probabilistic weather forecasting.
problem Probabilistic forecasting of weather.
method Two chained machine-learning steps: dimension reduction and density estimation using normalizing flows.
result The method produces accurate conditional forecast distributions for weather.
The combination of a CNN detector and a search framework forms the basis for local object/pattern detection. To handle the waste of regional information and the defective compromise between efficiency and accuracy, this paper proposes a probabilistic model with a powerful search framework. By mapping an image into a pr…
Paper interprets UMAP and t-SNE as probabilistic MAP inference.
problem Understanding and interpreting UMAP and t-SNE.
method Interprets UMAP and t-SNE as MAP inference methods corresponding to a probabilistic model of the graph Laplacian.
result Shows UMAP and t-SNE can be understood as probabilistic inference methods.
Quantum kernel improves probabilistic time series forecasting.
problem Quantifying uncertainty in probabilistic time series predictions.
method Integrates quantum kernel with Gaussian process regression.
result Quantum kernel enhances forecasting performance.
Study probabilistic safety of BNNs under adversarial attacks.
problem Evaluate vulnerability of BNNs to adversarial attacks.
method Relaxation techniques from non-convex optimization to compute probabilistic safety bounds.
result Certify probabilistic safety of BNNs with millions of parameters.
A novel GPUM constructs Gaussian Processes for unknown manifolds with probabilistic metrics.
problem High-dimensional data on unknown manifolds with non-Euclidean geometry.
method Bayesian Gaussian Processes latent variable models (BGPLVM), Riemannian geometry, probabilistic metric tensor, Brownian Motion.
result GPUM provides more accurate predictions on unknown manifolds compared to traditional methods.
Efficiently solves MRF inference problems with semidefinite programming.
problem Computing partition function or MAP estimate in binary and multi-class MRFs.
method Coordinate-descent-based fast semidefinite solver for SDPs.
result Substantially outperforms existing state-of-the-art methods in approximate inference.
A method for identifying NPWARX models with arbitrary domains using probabilistic mixture models.
problem Identifying hybrid system models with discontinuous maps.
method Probabilistic mixture model with a neural network for nonlinear partitioning and Expectation Maximization for parameter estimation.
result Demonstrated on a nonlinear piece-wise problem with discontinuous maps.
Many data-driven approaches exist to extract neural representations of functional magnetic resonance imaging (fMRI) data, but most of them lack a proper probabilistic formulation. We propose a group level scalable probabilistic sparse factor analysis (psFA) allowing spatially sparse maps, component pruning using automa…
New insights into risk aversion for complex decision models.
problem Understanding risk aversion in non-monotone decision models.
method Characterization of probabilistic risk aversion for generalized rank-dependent functions.
result Probabilistic risk aversion is determined by the distortion function, which is convex or scaled quantile-spread mixtures.
Paper introduces a novel map learning algorithm for domain translation and adaptation.
problem Learning a map between related data spaces that can be applied to out-of-sample data and satisfies application-specific constraints.
method Utilizes normalizing flows to parameterize a map that minimizes a probability distance and application-specific regularizers, solving a modified optimal transport problem.
result The proposed method (parOT) outperforms existing optimal transport approaches in domain adaptation and translation tasks.
Normalizing flows optimize Jacobian determinant for unique likelihood objective.
problem Optimizing normalizing flows for unique likelihood.
method Showed Jacobian determinant is unique for given distributions, leading to a unique global optimum. Used eigenvalues of auto-correlation matrix for explicit likelihood expression.
result Explicit expression of likelihood for flows, independent of neural network parameterization, with theoretical optimal value.
New method learns PDE solutions from low-fidelity data.
problem Challenges in learning PDE surrogates with scarce data.
method Flow matching in infinite-dimensional space with conditional neural operators.
result Accurately learns PDE solutions across different resolutions and fidelities.
The Dirichlet process mixture (DPM) is a ubiquitous, flexible Bayesian nonparametric statistical model. However, full probabilistic inference in this model is analytically intractable, so that computationally intensive techniques such as Gibb's sampling are required. As a result, DPM-based methods, which have considera…
New entropy-based objective for sparse coding improves learning.
problem Sparse coding with probabilistic priors and non-Gaussian observables.
method Derive a solely entropy-based learning objective for sparse coding parameters.
result Fully analytical ELBO objective for sparse coding with non-trivial posterior approximations.
Convex geometry has recently attracted great attention as a framework to formulate general probabilistic theories. In this framework, convex sets and affine maps represent the state spaces of physical systems and the possible dynamics, respectively. In the first part of this paper, we present a result on separation of …
Random G-expectationsmath.PR
We construct a time-consistent sublinear expectation in the setting of volatility uncertainty. This mapping extends Peng's G-expectation by allowing the range of the volatility uncertainty to be stochastic. Our construction is purely probabilistic and based on an optimal control formulation with path-dependent control …
Small neural networks embed arbitrary metric spaces into Gaussian mixtures.
problem Embedding arbitrary metric spaces into a fixed space with low distortion.
method Probabilistic transformers of small depth and width.
result Embeddings with low metric distortion for various metric spaces.
Describing the dimension reduction (DR) techniques by means of probabilistic models has recently been given special attention. Probabilistic models, in addition to a better interpretability of the DR methods, provide a framework for further extensions of such algorithms. One of the new approaches to the probabilistic D…
Framework predicts responses in misspecified systems using GPLFM and BNNs.
problem Predicting responses in dynamical systems with model misspecification.
method Integrates GPLFM and BNNs for uncertainty-aware inference and prediction.
result Systematic propagation of uncertainty from diagnosis to prediction.
This paper improves probabilistic latent models on hyperbolic spaces.
problem Uncertainty in predictions due to geodesics crossing low-data regions.
method Augmenting hyperbolic manifold with a pullback metric for probabilistic pullback metrics.
result Geodesics on pullback metric respect both geometry and data distribution, reducing uncertainty.
Much effort has been directed at algorithms for obtaining the highest probability configuration in a probabilistic random field model known as the maximum a posteriori (MAP) inference problem. In many situations, one could benefit from having not just a single solution, but the top M most probable solutions known as th…
We investigate the geometrical structure of probabilistic generative dimensionality reduction models using the tools of Riemannian geometry. We explicitly define a distribution over the natural metric given by the models. We provide the necessary algorithms to compute expected metric tensors where the distribution over…
Hybrid Bayesian neural networks use function uncertainty for probabilistic inference.
problem Uncertainty in neural network weights is hard to specify and interpret.
method Integrates probabilistic layers with standard deterministic layers for function uncertainty.
result Improves probabilistic inference by encoding function uncertainty.
Extends PCVM for multi-class classification with improved accuracy.
problem Lack of probabilistic outputs and contradictory predictions in multi-class classification.
method Proposes mPCVM with two learning algorithms: top-down and bottom-up.
result Superior performance, especially with many classes, validated on synthetic and benchmark data.
This short note highlights some links between two lines of research within the emerging topic of trustworthy machine learning: differential privacy and robustness to adversarial examples. By abstracting the definitions of both notions, we show that they build upon the same theoretical ground and hence results obtained …
New probabilistic invariants bound classical topological complexity and category.
problem Bounding classical topological complexity and category.
method Developed probabilistic variants of one-category and diagonal topological complexity.
result Identified new invariants with distributional category and complexity on Eilenberg-Mac Lane spaces.
ProbDR framework interprets DR algorithms as probabilistic inference.
problem Efficiently compressing high-dimensional data into lower dimensions.
method ProbDR variational framework that treats DR as probabilistic inference.
result ProbDR unifies various DR algorithms and enables probabilistic reasoning.
ICON learns differential equation operators from examples, revealing probabilistic inference.
problem Learning operators for differential equations from limited examples.
method Probabilistic operator learning using ICON architectures trained on diverse datasets.
result ICON implicitly performs Bayesian inference on solution operators.
We introduce two kernels that extend the mean map, which embeds probability measures in Hilbert spaces. The generative mean map kernel (GMMK) is a smooth similarity measure between probabilistic models. The latent mean map kernel (LMMK) generalizes the non-iid formulation of Hilbert space embeddings of empirical distri…
We introduce a new category of multivariate conditional generative models and demonstrate its performance and versatility in probabilistic time series forecasting and simulation. Specifically, the output of quantile regression networks is expanded from a set of fixed quantiles to the whole Quantile Function by a univar…