dynestyx: A library for probabilistic programming of dynamical systems
problem integrating state-space models into probabilistic programming languages
method a unified interface for specifying priors and performing inference
result principled uncertainty quantification for state and parameters
Bayesian framework for robust model discovery from noisy data.
problem Robust model discovery from noisy, sparse and irregular observations of nonlinear systems.
method Bayesian differential programming using Hamiltonian Monte Carlo and sparsity-promoting priors.
result Efficient inference of posterior distributions over plausible models with quantified uncertainty.
Unified approach to DP problems using Gumbel distribution and variational Bayesian inference.
problem Solving classical optimal path problems in a probabilistic framework.
method Gumbel distribution and variational Bayesian inference for latent optimal paths.
result Unified approach transforms DP problems into directed acyclic graphs with Gibbs distribution.
ExDBN learns dynamic Bayesian networks using mixed-integer programming.
problem Learning dynamic causal relationships from time series data.
method Score-based learning algorithm using mixed-integer quadratic programming with branch-and-cut method.
result The proposed method produces more accurate results than state-of-the-art approaches.
BNN-DP improves robustness analysis of Bayesian Neural Networks.
problem Ensuring robustness of Bayesian Neural Networks against adversarial attacks.
method Dynamic Programming applied to Bayesian Neural Networks as stochastic dynamical systems.
result BNN-DP provides tighter and more efficient bounds on prediction ranges compared to existing methods.
Bayesian approach infers signaling pathways from data.
problem Accurately understand cellular regulation processes.
method Dynamic Bayesian Network structure estimation using Markov Chain Monte Carlo.
result Efficient sampling of sparse graphs improves inference.
Novel framework for risk-sensitive reinforcement learning with robustness against uncertainty.
problem Risk-sensitive reinforcement learning with uncertainty in transition dynamics.
method Developed a risk-sensitive robust Markov decision process (RSRMDP), derived its Bellman equation, and proposed a Bayesian Dynamic Programming (Bayesian DP) algorithm.
result Demonstrated convergence to near-optimal policies and analyzed sample and computational complexities.
This paper optimizes sampling policies for Bayesian optimization to improve exploration and exploitation.
problem Improving the balance between exploration and exploitation in Bayesian optimization.
method Developed efficient methods to estimate and optimize non-myopic acquisition functions using rollout policies and stochastic gradient optimization.
result Efficient optimization of sampling policies leads to better performance in Bayesian optimization.
Develops a dynamic mean field theory for reinforcement learning.
problem Finite state and action Bayesian reinforcement learning in large state spaces.
method Analogies with statistical physics, interpreting probabilities as couplings and values as spins, solving mean field equations.
result State-action values are statistically independent in the asymptotic state space limit, with exact or approximate equations for computation.
Improves sampling efficiency for complex Bayesian models.
problem Inference challenges in hierarchical Gaussian-process models.
method Optimised Riemannian-manifold Hamiltonian Monte Carlo (RMHMC) with dynamic programming.
result Significant improvement in sampling efficiency and model evidence calculation.
We describe Bayesian Layers, a module designed for fast experimentation with neural network uncertainty. It extends neural network libraries with drop-in replacements for common layers. This enables composition via a unified abstraction over deterministic and stochastic functions and allows for scalability via the unde…
Exact causal network discovery is polynomial for sparse networks.
problem Finding the optimal causal Bayesian network from data is computationally hard.
method Pruning the search space using network properties, combined with dynamic programming and shortest-path searches.
result Exact discovery is polynomial for sparse causal Bayesian networks.
The design of multiple experiments is commonly undertaken via suboptimal strategies, such as batch (open-loop) design that omits feedback or greedy (myopic) design that does not account for future effects. This paper introduces new strategies for the optimal design of sequential experiments. First, we rigorously formul…
This study improves lookahead Bayesian optimization using rollout approximation.
problem Error propagation in lookahead Bayesian optimization due to model mis-specification.
method Proves rollout's improving nature in lookahead BO and provides guidelines for choosing the rolling horizon.
result Empirical results show rollout improves over myopic and non-myopic BO algorithms.
New methods improve global optimisation for expensive functions using lookahead strategies.
problem Optimising expensive functions without gradient info in high dimensions.
method Nonmyopic acquisition strategies based on approximate dynamic programming.
result Nonmyopic methods outperform myopic approaches in various applications.
Bayesian filtering optimizes portfolio weights over time with uncertain parameters.
problem Optimizing portfolios over long periods with unknown parameters.
method Bayesian filtering through dynamic linear models for dynamic parameter estimation.
result Bayesian updating improves portfolio performance and is practical.
Bayesian method synthesizes barrier certificates for unknown systems with latent states.
problem Certifying safety in systems with unknown dynamics and latent states.
method Bayesian inference with Metropolis-Hastings sampler and sum-of-squares program.
result Probabilistic validity of barrier certificates for unknown systems.
This paper computes exact posterior distributions of mixture weights in hierarchical Bayesian models.
problem Uncertainty in class membership or data-generating processes in heterogeneous data.
method Exact marginalization of mixture weights using dynamic programming and FFT for two components, and joint dynamic program for K >= 3 components.
result Exact posterior distributions of mixture weights are finite mixtures of Beta distributions, providing credible intervals and per-observation local false-discovery rates.
Probabilistic programming languages can simplify the development of machine learning techniques, but only if inference is sufficiently scalable. Unfortunately, Bayesian parameter estimation for highly coupled models such as regressions and state-space models still scales poorly; each MCMC transition takes linear time i…
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.
Efficiently selects top-m designs for various contexts using sequential sampling.
problem Optimizing selection of top-m designs across different contexts.
method Formulated as a stochastic dynamic programming problem, developed sequential sampling policy.
result Asymptotically optimal sampling ratios for efficient selection.
Many retailers today employ inventory management systems based on Re-Order Point Policies, most of which rely on the assumption that all decreases in product inventory levels result from product sales. Unfortunately, it usually happens that small but random quantities of the product get lost, stolen or broken without r…
This paper presents a fast Bayesian filtering technique for state estimation.
problem Bottleneck in Bayesian inference for state estimation from noisy sensor data.
method Processor-native uncertainty tracking for uncertainty propagation and inference.
result Deterministic approximate filtering with up to 805x speedup and competitive accuracy.
GP-NODE combines Gaussian processes and NeuralODEs for Bayesian system identification.
problem Bayesian systems identification from partial, noisy and irregular observations.
method Differentiable programming, Hamiltonian Monte Carlo, Gaussian Process priors, sparsity-promoting priors.
result Efficient inference of posterior distributions over plausible models with quantified uncertainty.
Bayesian approach for policy search in stochastic domains.
problem Policy search in stochastic domains.
method Nested probabilistic programs, Lightweight Metropolis-Hastings (LMH) adaptation.
result Similar quality policies learned with simpler algorithm.
This dissertation uses ILP to learn Bayesian network structures efficiently.
problem Learning the structure of Bayesian networks from data.
method Integer Linear Programming formulation with cluster constraints and cutting planes.
result The approach finds feasible solutions for Bayesian network structures efficiently.
One approach for constructing copula functions is by multiplication. Given that products of cumulative distribution functions (CDFs) are also CDFs, an adjustment to this multiplication will result in a copula model, as discussed by Liebscher (J Mult Analysis, 2008). Parameterizing models via products of CDFs has some a…
Bayesian approach models neurodegenerative diseases without clinical labels.
problem Personalized, predictive modeling of neurodegenerative diseases.
method Probabilistic programmed deep kernel learning combining Gaussian processes and neural networks.
result Surpasses deep learning in accuracy and timeliness of predicting neurodegeneration.
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…
PClean automates Bayesian data cleaning for specific datasets.
problem Bayesian inference for diverse and complex data cleaning.
method Domain-specific probabilistic programming language with custom models and inference.
result PClean programs outperform general-purpose PPLs in accuracy and runtime.
This paper proposes an online tree-based Bayesian approach for reinforcement learning. For inference, we employ a generalised context tree model. This defines a distribution on multivariate Gaussian piecewise-linear models, which can be updated in closed form. The tree structure itself is constructed using the cover tr…
Bayesian method approximates intractable stochastic programs with chance constraints.
problem Designing systems with stochastic constraints and chance constraints.
method Variational Bayesian approach to approximate posterior predictive integral.
result The solution set converges to the true solution set as the number of observations increases.
In this paper, we analyze dynamic programming as a novel approach to solve the problem of maximizing the profits of a bank. The mathematical model of the problem and the description of a bank's work is described in this paper. The problem is then approached using the method of dynamic programming. Dynamic programming m…
Paper tackles BNSL with IP, improving quality of solutions.
problem Bayesian Network Structure Learning (BNSL) with IP formulations.
method Inexact column generation using difference-of-submodular optimization.
result Improved solutions quality compared to state-of-the-art approaches.
Under a Bayesian framework, we formulate the fully sequential sampling and selection decision in statistical ranking and selection as a stochastic control problem, and derive the associated Bellman equation. Using value function approximation, we derive an approximately optimal allocation policy. We show that this poli…
Approximate dynamic programming algorithms, such as approximate value iteration, have been successfully applied to many complex reinforcement learning tasks, and a better approximate dynamic programming algorithm is expected to further extend the applicability of reinforcement learning to various tasks. In this paper w…
This paper improves dynamic hedging accuracy using genetic programming to forecast implied volatilities.
problem Improving the accuracy of dynamic hedging using implied volatilities.
method The paper uses genetic programming to forecast implied volatilities and tests the performance of these forecasts in dynamic hedging strategies.
result Genetic programming-generated implied volatilities improve hedging accuracy compared to static training methods.
MCMC methods for sampling from the space of DAGs can mix poorly due to the local nature of the proposals that are commonly used. It has been shown that sampling from the space of node orders yields better results [FK03, EW06]. Recently, Koivisto and Sood showed how one can analytically marginalize over orders using dyn…
The idea of computer vision as the Bayesian inverse problem to computer graphics has a long history and an appealing elegance, but it has proved difficult to directly implement. Instead, most vision tasks are approached via complex bottom-up processing pipelines. Here we show that it is possible to write short, simple …
Bayesian Experience Reuse improves learning from multiple experts.
problem Learning from multiple experts with conflicting goals.
method Bayesian neural networks with shared features to model uncertainty and derive a probability distribution over expert models.
result BERS method effectively samples demonstrations from the derived distribution to reuse them in new tasks.
New method uses dynamic programming for meta continual learning.
problem Challenges of generalization and catastrophic forgetting in sequential learning.
method Developed a theoretical framework using dynamic programming for meta continual learning.
result Theoretical and practical method achieves better accuracy than existing methods.
Bayesian optimization tackles non-convex, two-stage stochastic problems efficiently.
problem Solving non-convex, two-stage stochastic optimization problems with expensive, black-box evaluations.
method Knowledge-gradient-based acquisition function for joint optimization of first- and second-stage variables.
result Comparable and superior empirical results compared to alternatives.
Automates model comparison in probabilistic programming.
problem Manual derivations for model comparison are error-prone and time-consuming.
method Message passing on a Forney-style factor graph with a custom mixture node.
result Automates Bayesian model averaging, selection, and combination.
Bayesian hybrid models correct for missing physics in machine learning.
problem Systematic bias in machine learning models.
method Fusing physics-based insights with machine learning constructs, using Bayesian calibration and stochastic programming.
result Bayesian hybrid models outperform pure machine learning approaches with less data.
Probabilistic programs with dynamic computation graphs can define measures over sample spaces with unbounded dimensionality, which constitute programmatic analogues to Bayesian nonparametrics. Owing to the generality of this model class, inference relies on `black-box' Monte Carlo methods that are often not able to tak…
Celeste is a procedure for inferring astronomical catalogs that attains state-of-the-art scientific results. To date, Celeste has been scaled to at most hundreds of megabytes of astronomical images: Bayesian posterior inference is notoriously demanding computationally. In this paper, we report on a scalable, parallel v…
Exact Bayesian inference for discrete models using probability generating functions.
problem Discrete statistical models with infinite support and continuous priors.
method Probabilistic programming language with automatic differentiation and probability generating functions.
result Genfer tool provides exact solutions for a wide range of inference problems.
Research in reinforcement learning has produced algorithms for optimal decision making under uncertainty that fall within two main types. The first employs a Bayesian framework, where optimality improves with increased computational time. This is because the resulting planning task takes the form of a dynamic programmi…