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.
We consider controller-stopper problems in which the controlled processes can have jumps. The global filtration is represented by the Brownian filtration, enlarged by the filtration generated by the jump process. We assume that there exists a conditional probability density function for the jump times and marks given t…
Method learns optimal treatment sequences from observational data.
problem Optimal dynamic treatment regimes for public policies and medical interventions.
method Doubly robust classification-based approach via backward induction.
result Achieves optimal convergence rate of n^(-1/2) for welfare regret.
In this paper, we examine previous work on the naive Bayesian classifier and review its limitations, which include a sensitivity to correlated features. We respond to this problem by embedding the naive Bayesian induction scheme within an algorithm that c arries out a greedy search through the space of features. We hyp…
Bayesian units improve speech recognition with minimal parameters.
problem Improving speech recognition models with fewer parameters.
method Derived Bayesian recurrent units integrated into deep learning frameworks.
result Adding Bayesian units improves speech recognition performance.
New diagnostic tool for assessing approximate Bayesian inference.
problem Assessing the trustworthiness of approximate Bayesian inference.
method Reframe the problem in terms of incompatible conditional distributions and use Gibbs priors.
result The diagnostic tool can discover the inductive bias in various Bayesian models and approximations.
In this note we propose a new approach towards solving numerically optimal stopping problems via reinforced regression based Monte Carlo algorithms. The main idea of the method is to reinforce standard linear regression algorithms in each backward induction step by adding new basis functions based on previously estimat…
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…
We propose a numerical method for solving high dimensional fully nonlinear partial differential equations (PDEs). Our algorithm estimates simultaneously by backward time induction the solution and its gradient by multi-layer neural networks, while the Hessian is approximated by automatic differentiation of the gradient…
Goals for reinforcement learning problems are typically defined through hand-specified rewards. To design such problems, developers of learning algorithms must inherently be aware of what the task goals are, yet we often require agents to discover them on their own without any supervision beyond these sparse rewards. W…
This thesis explores supervised classification methods using Bayesian and exchangeability theories.
problem Assigning objects into predefined classes using training data and auxiliary information.
method Bayesian inductive theories and exchangeabilities (de Finetti and partition exchangeability).
result Optimal classifiers for different scenarios of object features and categories.
SGD-trained deep nets often generalize well due to a strong inductive bias towards low-error, low-complexity functions.
problem Understanding why overparameterized deep nets generalize well despite fitting training data perfectly.
method Empirical investigation of PSGD(f∣S) and PB(f∣S) for various architectures and datasets. result The probability of SGD-converging on a function consistent with training data correlates well with the Bayesian posterior probability of expressing that function.
FLUID uses flows to unify filtering and smoothing for complex systems.
problem Bayesian filtering and smoothing for high-dimensional nonlinear systems.
method FLUID encodes observation histories into a fixed summary statistic, using flows for filtering and smoothing.
result FLUID provides accurate approximations of filtering and smoothing distributions.
Discovering causal relationships is a hard task, often hindered by the need for intervention, and often requiring large amounts of data to resolve statistical uncertainty. However, humans quickly arrive at useful causal relationships. One possible reason is that humans extrapolate from past experience to new, unseen si…
Metalearned neural circuit performs inference over open classes.
problem Nonparametric Bayesian models' practical barriers in real-world applications.
method Extract inductive bias from nonparametric Bayesian model and transfer to neural network.
result Metalearned neural circuit achieves comparable or better performance than particle filter-based methods.
We propose new machine learning schemes for solving high dimensional nonlinear partial differential equations (PDEs). Relying on the classical backward stochastic differential equation (BSDE) representation of PDEs, our algorithms estimate simultaneously the solution and its gradient by deep neural networks. These appr…
This article presents a generic model for pricing financial derivatives subject to counterparty credit risk. Both unilateral and bilateral types of credit risks are considered. Our study shows that credit risk should be modeled as American style options in most cases, which require a backward induction valuation. To co…
Graph Convolutional Networks (GCNs) are powerful models for learning representations of attributed graphs. To scale GCNs to large graphs, state-of-the-art methods use various layer sampling techniques to alleviate the "neighbor explosion" problem during minibatch training. We propose GraphSAINT, a graph sampling based …
Proposes a new algorithm for Sparse Bayesian Learning connected to Stepwise Regression.
problem Sparse Bayesian Learning for probabilistic models.
method Coordinate ascent algorithm (RMP) for SBL, showing connection to Stepwise Regression.
result RMP's noise variance parameter limit connects to Stepwise Regression, with derived guarantees.
ACI identifies cause-effect relationships and causal influence ranges in dynamical systems.
problem Detecting and quantifying causal influence ranges in complex systems.
method Bayesian data assimilation and assimilative causal inference (ACI) to trace causes back from observed effects.
result Mathematically rigorous formulations of forward and backward causal influence ranges (CIRs) for nonlinear dynamical systems.
This paper introduces hierarchical Gaussian process priors for neural networks to capture weight correlations and inductive biases.
problem Capturing weight correlations and inductive biases in neural networks.
method Hierarchical Gaussian process priors with unit embeddings and input-dependent kernels.
result Hierarchical Gaussian process priors provide competitive predictive performance and desirable uncertainty estimates.
Two neural network methods solve the master equation for MFGs.
problem Approximating Nash equilibria in stochastic, finite-agent games.
method Backward induction and direct PDE tackling neural networks.
result Neural networks can approximate the master equation's solution.
This work presents an approach to automatically induction for non-greedy decision trees constructed from neural network architecture. This construction can be used to transfer weights when growing or pruning a decision tree, allowing non-greedy decision tree algorithms to automatically learn and adapt to the ideal arch…
New method stabilizes machine learning for physics-informed inverse problems.
problem Reconstructing physical quantities from PDE-compliant measurements.
method Physics-informed learning with smooth inductive bias.
result PDE operators stabilize variance and prevent overfitting in fixed dimensions.
Paper introduces IO-NPF for efficient Bayesian experimental design.
problem Efficient Bayesian experimental design in non-exchangeable settings.
method Inside-Out Nested Particle Filter (IO-NPF) for non-Markovian state-space models.
result IO-NPF achieves O(T2) computational complexity, improving efficiency. Deep density methods improve filtering in high-dimensional systems.
problem Nonlinear filtering in high-dimensional systems.
method Two deep density methods based on Feynman-Kac formulas and neural networks.
result Logarithmic deep backward stochastic differential equation filter outperforms classical methods in high dimensions.
The paper proposes a method to transfer knowledge across different settings using causal theory.
problem Learning transfer across similar but different settings.
method Bayesian perspective of causal theory induction, integrating instance-level associative learning and abstract-level structural causal knowledge.
result The proposed model achieved transfer behavior across trials and learning situations, unlike RL algorithms.
Learning-to-learn or meta-learning leverages data-driven inductive bias to increase the efficiency of learning on a novel task. This approach encounters difficulty when transfer is not advantageous, for instance, when tasks are considerably dissimilar or change over time. We use the connection between gradient-based me…
New method infers hidden states in continuous-time phenomena better than traditional models.
problem Traditional HSMM's are limited to discrete time grids and cannot handle irregularly spaced data.
method Formulated integro-differential forward and backward equations for CTSMC's, introduced scalable Viterbi-type algorithm.
result Efficiently solved equations for posterior marginals and path estimates.
Markov jump processes and continuous time Bayesian networks are important classes of continuous time dynamical systems. In this paper, we tackle the problem of inferring unobserved paths in these models by introducing a fast auxiliary variable Gibbs sampler. Our approach is based on the idea of uniformization, and sets…
The study examines how equivariance in networks affects generalization error using PAC-Bayesian bounds.
problem Understanding how equivariance in networks impacts generalization error.
method Utilized PAC-Bayesian analysis for equivariant networks, deriving norm-based bounds for generalization error.
result The bound indicates that using larger group size in the model improves generalization error.
Bayesian approach learns linear networks from high-dimensional data.
problem Learning high-dimensional linear Bayesian networks.
method Iterative estimation of topological ordering and parents using inverse partial covariance matrix with Bayesian regularization.
result The method successfully recovers network structure under certain conditions.
Bayesian algorithm discovers synthetic routes from target molecules.
problem Identifying synthetic routes from desired products.
method Bayesian inference and combinatorial optimization.
result Algorithm rediscovered 80.3% and 50.0% of known synthetic routes.
Bayesian approach improves neural network recurrence.
problem Improving neural network recurrence mechanisms.
method Introducing Bayesian recurrence relations and gates.
result Bayesian approach can perform as well as or better than conventional recurrent networks.
The paper analyzes stability and asymptotic behavior of hedging strategies in binomial and trinomial models.
problem Stability and asymptotic analysis of hedging strategies in incomplete financial models.
method Discrete-time Föllmer-Schweizer decomposition, perturbation analysis, and asymptotic approximation.
result Explicit formulas for leading order correction terms in asymptotic analysis.
Novel filter uses deep BSDE for nonlinear density approximation.
problem Nonlinear filtering problem.
method Bayesian filter based on deep BSDE and neural networks.
result Theoretical convergence rate confirmed in numerical examples.
Bayesian deep learning improves accuracy and calibration without sacrificing scalability.
problem Bayesian inference's potential for deep neural networks.
method Marginalization over optimization, using neural networks' inherent structure and inductive biases.
result Improvements in accuracy and calibration compared to standard training methods.
We consider a Bayesian method for learning the Bayesian network structure from complete data. Recently, Koivisto and Sood (2004) presented an algorithm that for any single edge computes its marginal posterior probability in O(n 2^n) time, where n is the number of attributes; the number of parents per attribute is bound…
Bayesian probability theory is one of the most successful frameworks to model reasoning under uncertainty. Its defining property is the interpretation of probabilities as degrees of belief in propositions about the state of the world relative to an inquiring subject. This essay examines the notion of subjectivity by dr…
The Bayesian framework is a well-studied and successful framework for inductive reasoning, which includes hypothesis testing and confirmation, parameter estimation, sequence prediction, classification, and regression. But standard statistical guidelines for choosing the model class and prior are not always available or…
Bayesian Additive Distribution Regression (DistBART) predicts distributions from grouped data.
problem Predicting distributions from grouped data with varying characteristics.
method Bayesian nonparametric approach using BART for modeling the regression function.
result Empirical and theoretical evidence supports DistBART's effectiveness in learning from low-dimensional marginals.
Bayesian Deep Learning tackles inverse problems with neural networks and approximate computations.
problem Solving inverse problems with indirect measurements and uncertainties.
method Bayesian Deep Learning, using neural networks and approximate computations.
result Effective solutions for inverse problems using Bayesian Deep Learning.
Graph-based kernels improve GP performance on graph data.
problem Improving Gaussian process performance on graph-structured data.
method Introduced graph neural network-inspired kernels into Gaussian processes.
result Graph convolutional networks are equivalent to certain GP kernels when infinitely wide.
PACOH improves meta-learning with theoretical guarantees and practical efficiency.
problem Meta-learning's generalization to unseen tasks is poorly understood, especially with limited meta-training tasks.
method PAC-Bayesian framework for deriving generalization bounds and developing PAC-optimal meta-learning algorithms.
result PACOH yields state-of-the-art performance in predictive accuracy and uncertainty estimation.
Paper identifies reductive MDPs, solving them in polynomial time.
problem Computational hardness of general MDPs and tractability of finite-horizon MDPs.
method Defines reductivity, a new class of SSPs, and develops a polynomial-time solution.
result Optimal policies can be found in polynomial time for reductive SSPs and MDPs.
Bayesian convolutional deep sets improve ambiguity in stationary process modeling.
problem Ambiguity in translation equivariant functional representations due to insufficient data points.
method Introduce Bayesian convolutional deep sets with task-dependent stationary prior.
result Improves representation quality compared to kernel smoother and non-parametric models.
Bayesian weight priors improve neural network learning of identity relations.
problem Neural networks struggle to learn abstract and systematic relations, especially identity relations.
method Extended RBP approach using Bayesian weight priors as a regularization term.
result Bayesian weight priors lead to perfect generalization for identity relations and do not hinder standard neural network learning.
The paper analyzes trade execution strategies for large traders in a stochastic market environment.
problem Analyzing trade execution strategies in a stochastic market with price impact.
method Formulated a Markov game model and used backward induction method of dynamic programming.
result Explicit closed-form execution strategy at Markov perfect equilibrium.