Study of filtering and smoothing in submanifolds of Euclidean space.
problem Filtering and smoothing in continuous-discrete time on submanifolds.
method Formal expressions and projection approach for prediction and smoothing.
result Agreement with classical results for prediction, differences for smoothing.
DualSMC combines filtering and planning for continuous POMDPs.
problem Handling multi-modal state distributions and uncertainty in continuous POMDPs.
method DualSMC network that combines SMC for filtering and planning, with adversarial particle filter and uncertainty-dependent policy.
result DualSMC effectively handles complex observations and remains interpretable.
Transformers can solve complex filtering problems for non-Gaussian signals.
problem Non-linear and non-Markovian filtering problems for conditionally Gaussian signals.
method Continuous-time transformer models called filterformers.
result Filterformers can approximate the conditional law of non-Markovian and conditionally Gaussian signal processes.
We consider a Hidden Markov Model (HMM) where the integrated continuous-time Markov chain can be observed at discrete time points perturbed by a Brownian motion. The aim is to derive a filter for the underlying continuous-time Markov chain. The recursion formula for the discrete-time filter is easy to derive, however i…
Improves music composition with user-defined constraints using continuous time models.
problem Combining sequence models with user-defined constraints in continuous time.
method Introduces a novel particle filter scheme for continuous time point processes.
result The particle filter scheme yields superior results in a human listening test.
We seek to learn an effective policy for a Markov Decision Process (MDP) with continuous states via Q-Learning. Given a set of basis functions over state action pairs we search for a corresponding set of linear weights that minimizes the mean Bellman residual. Our algorithm uses a Kalman filter model to estimate those …
Regime-switching models, in particular Hidden Markov Models (HMMs) where the switching is driven by an unobservable Markov chain, are widely-used in financial applications, due to their tractability and good econometric properties. In this work we consider HMMs in continuous time with both constant and switching volati…
Paper proposes a new Taylor moment expansion for non-linear Gaussian filtering and smoothing.
problem Non-linear Gaussian filtering and smoothing in continuous-discrete state-space models.
method Taylor moment expansion (TME) for moment functions directly and in time variable.
result Significantly outperforms state-of-the-art methods in terms of estimation accuracy and numerical stability.
New algorithm for aggregate inference in HMMs with continuous observations.
problem Inference in large populations with indistinguishable individuals and continuous measurements.
method Continuous observation collective forward-backward algorithm extending existing discrete case algorithm.
result Efficacy demonstrated through numerical experiments.
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…
SchNet models quantum interactions using continuous filters, outperforming traditional methods.
problem Capturing continuous atomic positions in molecules without losing physical information.
method Continuous-filter convolutional neural network architecture in SchNet.
result SchNet models both total energy and interatomic forces with rotationally invariant predictions and a smooth potential energy surface.
Neural Jump ODE improves continuous-time prediction and filtering of irregularly sampled time series.
problem Theoretical guarantees for continuous-time prediction and filtering of irregularly observed time series.
method Introducing Neural Jump ODE (NJ-ODE) that models conditional expectation between observations with neural ODEs and jumps.
result Theoretical guarantees for the L2-optimal prediction are provided, showing convergence of model output to optimal prediction. Paper solves POMDPs in continuous time and discrete spaces.
problem Optimal decision making in discrete state and action space systems under partial observability.
method Combining optimal filtering theory and deep learning to solve a Hamilton-Jacobi-Bellman equation.
result Derives a mathematical description and solution approach for continuous-time POMDPs.
Paper proposes continuous residual layers for graph neural networks.
problem Low-pass filtering effect in GCN-based models.
method Integrates Ordinary Differential Equations (ODE) to produce outputs of continuous residual layers.
result Continuous residual layers achieve better results than non-residual modules in multiple layers.
New sampling-based approach for filtering problems using multiplicative Gaussian functions.
problem Approximate inference in filtering problems.
method Approximates distribution with a weighted sum of continuous functions using sampling for multiplications.
result Preliminary experiments show potential of the new method compared to particle filters.
Unified framework for inference in complex nonlinear processes.
problem Challenges in inferring nonlinear continuous stochastic processes with sparse observations and complex topologies.
method Neural Backward Filtering Forward Guiding (NBFFG) framework that constructs a variational posterior using a proxy linear-Gaussian process.
result Empirical results show NBFFG outperforms baselines on synthetic benchmarks and high-dimensional phylogenetic analysis tasks.
In this paper we introduce a projection method for the space of probability distributions based on the differential geometric approach to statistics. This method is based on a direct L2 metric as opposed to the usual Hellinger distance and the related Fisher Information metric. We explain how this apparatus can be used…
Gradient filters track moving parameters under noisy data and misspecification.
problem Tracking multidimensional time-varying parameters under noisy observations and model misspecification.
method Gradient-based filters update parameters using the gradient of a postulated objective function, evaluated at either the predicted or updated parameters.
result Novel sufficient conditions for exponential stability of the filtered parameter path, and finite-sample and asymptotic mean squared error bounds.
We examine some differential geometric approaches to finding approximate solutions to the continuous time nonlinear filtering problem. Our primary focus is a new projection method for the optimal filter infinite dimensional Stochastic Partial Differential Equation (SPDE), based on the direct L2 metric and on a family o…
PFPN uses particle filtering to improve character control in physics-based simulations.
problem Premature commitment to suboptimal actions in high-dimensional continuous control problems for articulated characters.
method Proposes a particle-based action policy using particle filtering to dynamically explore and discretize the action space.
result Demonstrates better imitation performance and robustness to external perturbations compared to Gaussian policies.
We revisit the problem of estimating the parameters of a partially observed diffusion process, consisting of a hidden state process and an observed process, with a continuous time parameter. The estimation is to be done online, i.e. the parameter estimate should be updated recursively based on the observation filtratio…
Paper develops unbiased gradient estimator for continuous-time models.
problem Estimating unbiased gradient of log-likelihood for continuous-time models.
method Doubly randomized scheme with coupled conditional particle filter (CCPF).
result Unbiased gradient estimate facilitates gradient-based algorithms.
Develops Bayesian filtering for online learning and related problems.
problem Sequential machine learning challenges, especially non-stationarity, model misspecification, and high dimensionality.
method Modular adaptive framework, provably robust filter, and sequential parameter updates.
result Improved performance in dynamic, high-dimensional, and misspecified models.
We revisit the development of grid based recursive approximate filtering of general Markov processes in discrete time, partially observed in conditionally Gaussian noise. The grid based filters considered rely on two types of state quantization: The \textit{Markovian} type and the \textit{marginal} type. We propose a s…
We present a general theory of fractal transformations and show how it leads to a new type of method for filtering and transforming digital images. This work substantially generalizes earlier work on fractal tops. The approach involves fractal geometry, chaotic dynamics, and an interplay between discrete and continuous…
In this paper we use continuous family of multisections of the moduli space of pseudo holomorphic discs to partially improve, in the case of real coefficient, the construction of Lagrangian Floer cohomology of which the author developed jointly with Oh-Ohta-Ono. Namely we associate cyclically symmetric filtered A infin…
A modular cash-overlay rule for allocating between a fixed growth-defensive risky sleeve and interest-bearing cash.
problem Drawdown control
method Continuous cash-overlay filters
result Earnings an 18.83% CAGR versus 16.62% for 100% R
New deep learning method approximates Benes filter model.
problem Approximating high-dimensional SPDEs for filtering.
method Deep learning mesh-free neural network representation.
result First study of neural network method for Benes model.
CRUs model irregular time series with continuous hidden states.
problem Handling irregular time intervals in sequential data.
method Continuous Recurrent Units (CRUs) that integrate hidden states via a linear stochastic differential equation.
result CRUs outperform methods based on neural ordinary differential equations in irregular time series interpolation.
Enhances SBM with continuous attributes for better network analysis.
problem Community detection in networks with multiple continuous attributes.
method Augmented stochastic block model with multivariate Gaussian parameters.
result Satisfactory performance in link prediction and collaborative filtering tasks.
Impute missing events in continuous-time sequences using particle smoothing.
problem Missing events in continuous-time sequences.
method Particle smoothing with trainable bidirectional LSTM proposals.
result Imputed sequences have low Bayes risk compared to ground truth.
We present a data-efficient reinforcement learning algorithm resistant to observation noise. Our method extends the highly data-efficient PILCO algorithm (Deisenroth & Rasmussen, 2011) into partially observed Markov decision processes (POMDPs) by considering the filtering process during policy evaluation. PILCO conduct…
This paper tackles continuous domain adaptation with a new approach.
problem Learning in non-stationary environments, especially domain drift.
method Variational domain-agnostic feature replay, composed of inference, generative, and solver modules.
result Demonstrates the effectiveness of the proposed approach for practical usage.
New wavelet frames constructed from reproducing kernels for continuous and discrete domains.
problem Generating wavelet frames on non-Euclidean structures.
method Spectral filtering of integral operators associated with reproducing kernels.
result Discrete frames as Monte Carlo estimates of continuous frames, with finite-sample rates derived.
Paper uses optimal transport for Bayesian filtering, deriving new EnKF and FPF formulations.
problem Bayesian filtering for nonlinear systems with non-Gaussian observations.
method Optimal transport theory applied to Bayes' law, constructing Brenier maps.
result New variational formulations of EnKF and FPF for non-Gaussian settings.
Kernel-based Bayesian filter for nonlinear systems using infinite-dimensional operators.
problem Modeling and predicting nonlinear dynamical systems.
method Functional Bayesian perspective, reproducing kernel Hilbert space, Gaussian kernel.
result Effective approximation and accurate results for nonlinear systems.
This paper introduces the kernel mixture network, a new method for nonparametric estimation of conditional probability densities using neural networks. We model arbitrarily complex conditional densities as linear combinations of a family of kernel functions centered at a subset of training points. The weights are deter…
Proposes a nonparametric approach for inferring spike train filters.
problem Modeling neuron information encoding from electrophysiological recordings.
method Gaussian process framework for joint inference of filters and hyperparameters.
result Automatic learning of filter temporal span and stimulus/history filters.
The paper uses filtering techniques to predict rating transitions.
problem Analyzing the effect of business cycles on rating transitions.
method Point process filtering framework to infer latent factor states.
result Efficient estimation of latent factor parameters for real-time detection of economic changes.
A method for optimal Bayesian filtering using progressive particle flow and optimal transport maps.
problem Optimizing Bayesian filtering with deterministic particles to avoid degeneration.
method Progressive flow of particles through a sequence of sub-steps, each using an optimal transport map to replace non-equally weighted particles with equally weighted ones.
result The method avoids particle degeneration and simplifies the filtering process by not requiring inversions or monotonicity constraints.
We extend the Fourier cosine method to discrete probability distributions, achieving faster convergence rates.
problem Extending Fourier cosine method to discrete probability distributions.
method Spectral filters and convergence rates analysis.
result Spectral filters achieve one order faster convergence rates than previously recognized.
ABHT boosts regression by filtering regions with different smoothness.
problem Improving regression performance through local adaptivity.
method Gradient boosting with adaptive histogram transform.
result ABHT converges faster than PEHT in Hölder continuous spaces.
Algorithm simulates counterfactuals for fairness analysis.
problem Analytical intractability of counterfactuals in conditional distributions.
method Proposes an algorithm using particle filtering for discrete and continuous variables.
result Asymptotically valid inference for counterfactuals.
MoE-F combines LLMs online for better time-series prediction.
problem Combining multiple LLMs for online time-series prediction.
method Time-adaptive stochastic filtering techniques to combine experts.
result MoE-F achieves 17% absolute and 48.5% relative F1 measure improvement.
New research connects evolutionary dynamics to Bayesian learning.
problem Connecting evolutionary biology and Bayesian learning.
method Rigorous mathematical proof using Kushner-Stratonovich equation and gradient flows.
result Discrete time filtering equations converge to Stratonovich interpretation of Kushner-Stratonovich equation.
A new approach to symbol calculus on filtered manifolds using C∗-algebras.
problem Symbol calculus on filtered manifolds with local isomorphism to stratified Lie groups.
method Establishing a surjective ∗-homomorphism between a C∗-algebra bundle and the algebra of bounded continuous sections. result Existence of a surjective ∗-homomorphism sym_M: Π_M → C_b(E_hom) with specific kernel properties. End-to-end network predicts and aligns continuous emotion labels.
problem Inconsistent alignment of continuous emotion labels with speech signals.
method Convolutional neural network with a multi-delay sinc layer.
result State-of-the-art results in predicting and aligning continuous emotion labels.
Proposes continuous convolution layers for flexible feature map resizing.
problem Fixed stride limitations in discrete convolution layers.
method Introduces Continuous Convolution (CC) layers that use learned continuous functions.
result Dynamic and consistent resizing of feature maps at any scale, non-integer and axis-dependent.