Study Markov cubature rules for polynomial processes.
problem Tractability of path-dependent tasks in polynomial process models.
method Discretizations using finite state Markov processes with moment matching conditions.
result Markov cubature rules aid American option pricing.
Paper introduces cubature method for stochastic Volterra equations.
problem Solving stochastic Volterra integral equations efficiently.
method Derive stochastic Taylor expansion, introduce cubature measure.
result Cubature method is more efficient than Euler scheme under certain conditions.
Develops trinomial models using cubature methods for financial derivative pricing.
problem Pricing financial derivatives in complex stochastic market models.
method Cubature methods applied to Wiener space for constructing trinomial models.
result Numerical solutions compare favorably with Black-Scholes model.
The paper develops methods to approximate quantities of interest in insurance models using deterministic integration.
problem Computing quantities of interest in insurance models, such as the probability of ruin and insurance company value.
method Adapting the problem to allow for deterministic numerical integration algorithms, including quasi-Monte Carlo rules and smoothing techniques.
result Convergence result justifying phase-type approximations on the process level.
Cubature on Wiener space [Lyons, T.; Victoir, N.; Proc. R. Soc. Lond. A 8 January 2004 vol. 460 no. 2041 169-198] provides a powerful alternative to Monte Carlo simulation for the integration of certain functionals on Wiener space. More specifically, and in the language of mathematical finance, cubature allows for fast…
The study characterizes kernel spaces on hyperspheres, impacting cubature algorithms.
problem Characterizing kernel spaces on hyperspheres for cubature algorithms.
method Characterization of Sobolev spaces and reproducing kernel Hilbert spaces over hyperspheres.
result Direct consequences for kernel cubature and worst-case error rates.
Cubature methods, a powerful alternative to Monte Carlo due to Kusuoka~[Adv.~Math.~Econ.~6, 69--83, 2004] and Lyons--Victoir~[Proc.~R.~Soc.\\Lond.~Ser.~A 460, 169--198, 2004], involve the solution to numerous auxiliary ordinary differential equations. With focus on the Ninomiya-Victoir algorithm~[Appl.~Math.~Fin.~15, 1…
New filters improve radar target inference in complex scenarios.
problem Improving radar target inference in highly non-linear system models.
method Developed inverse cubature Kalman filter (I-CKF), inverse quadrature Kalman filter (I-QKF), and inverse cubature-quadrature Kalman filter (I-CQKF) for non-linear systems.
result Numerical experiments show improved estimation accuracy compared to existing methods.
This article is concerned with Gaussian process quadratures, which are numerical integration methods based on Gaussian process regression methods, and sigma-point methods, which are used in advanced non-linear Kalman filtering and smoothing algorithms. We show that many sigma-point methods can be interpreted as Gaussia…
Paper develops a high-order recombination algorithm for financial modeling.
problem Creating accurate approximations of stochastic differential equations in finance.
method High-order recombination method applied to practical financial problems.
result Algorithm effectively avoids explosive growth in support cardinality for high-order approximations.
New algorithms minimize MMD to approximate probability measures efficiently.
problem Approximating probability measures by representative point sets.
method Sequential greedy minimization of maximum mean discrepancy (MMD) over candidate sets, with mini-batch variants.
result Consistency of proposed algorithms and mini-batch variants established.
Different directed acyclic graphs (DAGs) may be Markov equivalent in the sense that they entail the same conditional independence relations among the observed variables. Meek (1995) characterizes Markov equivalence classes for DAGs (with no latent variables) by presenting a set of orientation rules that can correctly i…
Bayesian method infers local rules for collective animal movement.
problem Learn local rules governing long-term group behaviors.
method Bayesian Inverse Reinforcement Learning with Linearly-Solvable Markov Decision Process.
result Recover true costs and find value of collective movement.
NMLNs use neural networks to learn relational structure from data.
problem Learning implicit rules from data without explicit logic rules.
method Combines Markov logic with neural networks to learn relational structure.
result NMLNs can predict in settings without explicit logic rules.
We present a general probabilistic perspective on Gaussian filtering and smoothing. This allows us to show that common approaches to Gaussian filtering/smoothing can be distinguished solely by their methods of computing/approximating the means and covariances of joint probabilities. This implies that novel filters and …
New rule reduces exploration regret to logarithmic, improving bad episode handling.
problem Improving exploration regret in average reward MDPs.
method Replacing Doubling Trick with Vanishing Multiplicative rule in EVI-based algorithms.
result Regret is logarithmic under the new rule, significantly better than linear.
Proposes PRMs for interpreting financial risk concept drift.
problem Concept drift in high-stakes predictions like credit risk.
method Probabilistic Rule Models (PRMs) using Markov Logic Networks.
result Interpretable rules explain borrower risk changes.
Quantum models use complex Hilbert spaces for uncertainty.
problem Modeling dynamics in continuous-valued features.
method Quantum Graphical Models (QGMs) and Hilbert Space Embedding (HSE).
result HSE-HQMMs are competitive with state-of-the-art models.
Study restricts causal graphs with expert knowledge.
problem Restricting causal graphs to include expert orientation knowledge.
method Prove properties, present new orientation rules, develop algorithms.
result Shows how to uniquely represent restricted essential ancestral graphs.
pLogicNet combines logic rules and embeddings for efficient knowledge graph reasoning.
problem Efficiently predicting missing facts in knowledge graphs.
method Combines Markov Logic Networks with knowledge graph embeddings using variational EM algorithm.
result pLogicNet outperforms traditional methods on multiple knowledge graphs.
Paper finds optimal selling rule for pairs trading with stock constraints.
problem Identifying the best time to sell in pairs trading of stocks.
method Optimal pairs-trading selling rule with constraints on trading.
result Closed-form solution for optimal policy determined by a threshold curve.
In this paper, we present a novel and general framework called {\it Maximum Entropy Discrimination Markov Networks} (MaxEnDNet), which integrates the max-margin structured learning and Bayesian-style estimation and combines and extends their merits. Major innovations of this model include: 1) It generalizes the extant …
This study uses HMM and RL to dynamically allocate equities, Treasuries, and gold based on market regimes.
problem Developing a dynamic portfolio allocation strategy for different market conditions.
method Characterizes market regimes using Markov switching models and HMM, then applies RL for allocation decisions.
result RL-based allocation outperforms passive strategies, providing lower drawdowns and higher Sharpe ratios.
Identifies policy space of learning agents from demonstrations.
problem Identifying the policy parameters a learning agent can control.
method Statistical testing and Configurable Markov Decision Processes.
result Probabilistic analysis of simplified identification rule for linear policies.
Develops a new framework for conditional independence.
problem Generalizing previous notions of conditional independence.
method Introduces transition probability spaces and transitional random variables.
result Satisfies all desired relevance relations except symmetry.
Flexible log file parsing using HMM adapts to evolving content.
problem Dynamic log file processing with evolving content.
method Modeling frequent patterns into HMM for flexible log file parsing.
result High accuracy (over 99%) in parsing different system log files.
This paper is concerned with an optimal stock selling rule under a Markov chain model. The objective is to find an optimal stopping time to sell the stock so as to maximize an expected return. Solutions to the associated variational inequalities are obtained. Closed-form solutions are given in terms of a set of thresho…
We describe various sets of conditional independence relationships, sufficient for qualitatively comparing non-vanishing squared partial correlations of a Gaussian random vector. These sufficient conditions are satisfied by several graphical Markov models. Rules for comparing degree of association among the vertices of…
RML improves generative modeling of complex distributions.
problem Learning complex distributions in applications.
method RML defines a forward process to a known distribution, then learns a reverse Markov process.
result RML efficiently captures complex distributions in simulations and climate data.
Bayesian RL tackles uncertainty with deep generative models and sequential samplers.
problem Optimal decision-making in uncertain environments with limited data.
method Bayesian approach using deep generative models and prequential scoring rule for posterior inference. Policy learning via expected Thompson sampling.
result Improves policy learning in high-dimensional parameter spaces and continuous action spaces.
Study optimal adaptive allocation for multi-armed bandits with Markovian rewards.
problem Optimal adaptive allocation for multi-armed bandits with Markovian rewards.
method Round-robin Kullback-Leibler upper confidence bounds for optimal adaptive allocation.
result Logarithmic dependence of regret on time horizon, asymptotically optimal.
Paper introduces FDM for efficient training of Neural SDEs.
problem Training Neural SDEs using existing methods is computationally expensive and unstable.
method Developed a novel scoring rule called Finite Dimensional Matching (FDM) to bypass signature kernels and reduce training complexity.
result FDM achieves superior performance in terms of computational efficiency and generative quality.
New method for nonlinear filtering and smoothing using factor graphs.
problem Handling deterministic nonlinear transformations in factor graphs.
method Approximate Gaussian message passing rules for factor graphs with Markov property.
result Proposed nonlinear modified Bryson-Frazier smoother.
New algorithms identify best policies in discounted linear MDPs efficiently.
problem Identifying the best policy in discounted linear MDPs with limited samples.
method Derive lower bounds and devise simple yet near-optimal algorithms.
result Upper bound on sample complexity matches existing bounds.
New transport method simplifies cutoff phenomenon for Markov processes.
problem Understanding the cutoff phenomenon for Markov processes.
method A new W-TV transport inequality combined with a parabolic regularization estimate.
result Recovery and extension of previous results on cutoff phenomena.
New algorithms for high-dimensional HMMs reduce complexity by discarding non-local factors.
problem High-dimensional HMMs are computationally expensive to filter and smooth.
method Approximate filtering and smoothing via locality in factor graphs, avoiding exponential cost.
result Error bounds in local total variation norm are dimension-free, improving scalability.
In this paper we propose a novel approach for learning from data using rule based fuzzy inference systems where the model parameters are estimated using Bayesian inference and Markov Chain Monte Carlo (MCMC) techniques. We show the applicability of the method for regression and classification tasks using synthetic data…
The pseudo-likelihood method is one of the most popular algorithms for learning sparse binary pairwise Markov networks. In this paper, we formulate the L1 regularized pseudo-likelihood problem as a sparse multiple logistic regression problem. In this way, many insights and optimization procedures for sparse logistic…
We introduce a new braid-theoretic framework with which to understand the Legendrian and transversal classification of knots, namely a Legendrian Markov Theorem without Stabilization which induces an associated transversal Markov Theorem without Stabilization. We establish the existence of a nontrivial knot-type specif…
New framework improves stochastic optimization for variational inference.
problem Improving variational posterior approximations in high-dimensional models.
method Developed a robust stochastic optimization framework using Markov chains.
result Demonstrated improved accuracy and robustness across diverse models.
We propose a new statistical model for computational linguistics. Rather than trying to estimate directly the probability distribution of a random sentence of the language, we define a Markov chain on finite sets of sentences with many finite recurrent communicating classes and define our language model as the invarian…
The paper develops a stationary-distribution theory for Random Forest ensemble size selection.
problem Determining the optimal number of trees in Random Forests.
method Modeling the ensemble size as a birth-death Markov chain and deriving its stationary distribution.
result The stationary ensemble size B∗ scales as O(ε−2) as ε↓0. Researchers adaptively analyze market regimes to reveal investor behavior shifts.
problem Market relationships shift across different regimes, affecting investor behavior.
method Combining Kalman filtering, Markov-switching, and asymmetric response estimation.
result Foreign investors' predictive power increases during crises, while individual investors react more strongly to positive shocks.
Concept Relation Discovery and Innovation Enabling Technology (CORDIET), is a toolbox for gaining new knowledge from unstructured text data. At the core of CORDIET is the C-K theory which captures the essential elements of innovation. The tool uses Formal Concept Analysis (FCA), Emergent Self Organizing Maps (ESOM) and…
Study identifies two borrowing patterns in UK payday loan users.
problem Financial vulnerability of payday loan users.
method Two-state hidden Markov model (HMM) using Open Banking data.
result 36.4% of borrowers experience high-intensity exposure for 12 weeks or more.
Kernel quadrature improves CRPS estimation for probabilistic time-series forecasting.
problem Intractable integrations in CRPS evaluation metrics lead to improper rankings of forecasting models.
method Introduced kernel quadrature approach for unbiased CRPS estimation and scalable computation.
result Our approach consistently outperforms existing CRPS estimators.
Paper proposes FHMM for better attacker behaviour profiling.
problem Modeling attacker behaviour for better predictive power.
method Semi-supervised Fusion Hidden Markov Model (FHMM).
result FHMM provides comparable accuracy to Deep RNN at lower training time.
New algorithm detects and discards faulty updates in federated learning.
problem Byzantine failures, biased local datasets, and poisoning attacks in federated learning.
method Adaptive Federated Averaging with Hidden Markov Model for quality update detection.
result Significantly more robust to faulty, noisy, and malicious participants.