A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Unified framework for discrete diffusion modeling with flexible noising processes.
problem Efficient modeling of large discrete state spaces with arbitrary corruption dynamics.
method Generalized Discrete Diffusion from Snapshots (GDDS) framework that supports uniformization for fast noising and snapshot-based ELBO for reverse process.
result GDDS outperforms existing discrete diffusion methods in training efficiency and generation quality.
We consider the inverse problem of reconstructing the posterior measure over the trajec- tories of a diffusion process from discrete time observations and continuous time constraints. We cast the problem in a Bayesian framework and derive approximations to the posterior distributions of single time marginals using vari…
This study bridges discrete and continuous state spaces using the Ehrenfest process and diffusion models.
problem Understanding the relationship between discrete and continuous state spaces in stochastic processes.
method Investigates time-continuous Markov jump processes on discrete state spaces and their correspondence to state-continuous diffusion processes.
result The time-reversal of the Ehrenfest process converges to the time-reversed Ornstein-Uhlenbeck process, bridging discrete and continuous state spaces.
The health state assessment and remaining useful life (RUL) estimation play very important roles in prognostics and health management (PHM), owing to their abilities to reduce the maintenance and improve the safety of machines or equipment. However, they generally suffer from this problem of lacking prior knowledge to …
Many nonlinear extensions of the Kalman filter, e.g., the extended and the unscented Kalman filter, reduce the state densities to Gaussian densities. This approximation gives sufficient results in many cases. However, this filters only estimate states that are correlated with the observation. Therefore, sequential esti…
Fluid approximations have seen great success in approximating the macro-scale behaviour of Markov systems with a large number of discrete states. However, these methods rely on the continuous-time Markov chain (CTMC) having a particular population structure which suggests a natural continuous state-space endowed with a…
This paper investigates the position (state) distribution of the single step binomial (multi-nomial) process on a discrete state / time grid under the assumption that the velocity process rather than the state process is Markovian. In this model the particle follows a simple multi-step process in velocity space which a…
We investigate the statistical complexity of estimating the parameters of a discrete-state Markov chain kernel from a single long sequence of state observations. In the finite case, we characterize (modulo logarithmic factors) the minimax sample complexity of estimation with respect to the operator infinity norm, while…
In this letter we borrow from the inference techniques developed for unbounded state-cardinality (nonparametric) variants of the HMM and use them to develop a tuning-parameter free, black-box inference procedure for Explicit-state-duration hidden Markov models (EDHMM). EDHMMs are HMMs that have latent states consisting…
Change-point analysis is a flexible and computationally tractable tool for the analysis of times series data from systems that transition between discrete states and whose observables are corrupted by noise. The change-point algorithm is used to identify the time indices (change points) at which the system transitions …
Bayesian inference of discrete component states in civil infrastructures using PGMs and GNNs.
problem Inferring discrete states of civil infrastructure components from measurable responses is an ill-posed inverse problem.
method The study proposes a novel Bayesian inversion paradigm based on Probabilistic Graphical Models (PGMs) and Graph Neural Networks (GNNs). PGMs are used to model the problem, with parameters learned from data and structural topology prior. Inference is accomplished by GNNs, and a graph property-based training strategy is developed.
result The proposed framework effectively solves the challenges of inferring the posterior PDF for discrete variables in high-dimensional problems.
NCDSSM models irregularly sampled time series with improved imputation and forecasting.
problem Accurate modeling of irregularly sampled time series with missing observations.
method Neural Continuous-Discrete State Space Model (NCDSSM) with amortized inference for auxiliary variables and flexible dynamic state parameterizations.
result Improved imputation and forecasting performance on multiple benchmark datasets.
Contagions such as the spread of popular news stories, or infectious diseases, propagate in cascades over dynamic networks with unobservable topologies. However, "social signals" such as product purchase time, or blog entry timestamps are measurable, and implicitly depend on the underlying topology, making it possible …
A new method generates mixed-type features in tabular data with improved realism and accuracy.
problem Generating mixed-type features combining discrete and continuous data is challenging.
method A cascaded approach: first generates low-resolution categorical and coarse numerical features, then uses these in a high-resolution flow matching model.
result The model significantly improves detection scores, generating more realistic samples and capturing distributional details.
Active inference is a process theory of the brain that states that all living organisms infer actions in order to minimize their (expected) free energy. However, current experiments are limited to predefined, often discrete, state spaces. In this paper we use recent advances in deep learning to learn the state space an…
For an autonomous agent, executing a poor policy may be costly or even dangerous. For such agents, it is desirable to determine confidence interval lower bounds on the performance of any given policy without executing said policy. Current methods for exact high confidence off-policy evaluation that use importance sampl…
Multi-stage financial decision optimization under uncertainty depends on a careful numerical approximation of the underlying stochastic process, which describes the future returns of the selected assets or asset categories. Various approaches towards an optimal generation of discrete-time, discrete-state approximations…
Stochastic domains often involve risk-averse decision makers. While recent work has focused on how to model risk in Markov decision processes using risk measures, it has not addressed the problem of solving large risk-averse formulations. In this paper, we propose and analyze a new method for solving large risk-averse …
We consider the problem of estimating the topology of spatial interactions in a discrete state, discrete time spatio-temporal graphical model where the interactions affect the temporal evolution of each agent in a network. Among other models, the susceptible, infected, recovered (SIR) model for interaction events fal…
This paper proposes new search algorithms for counterfactual explanations based upon mixed integer programming. We are concerned with complex data in which variables may take any value from a contiguous range or an additional set of discrete states. We propose a novel set of constraints that we refer to as a "mixed pol…
Stochastic gradient MCMC (SG-MCMC) algorithms have proven useful in scaling Bayesian inference to large datasets under an assumption of i.i.d data. We instead develop an SG-MCMC algorithm to learn the parameters of hidden Markov models (HMMs) for time-dependent data. There are two challenges to applying SG-MCMC in this…
Model reduction of Markov processes is a basic problem in modeling state-transition systems. Motivated by the state aggregation approach rooted in control theory, we study the statistical state compression of a discrete-state Markov chain from empirical trajectories. Through the lens of spectral decomposition, we study…