Adaptive LASSO improves model selection for functional geostatistical data.
problem Modeling georeferenced data with spatiotemporal dynamics and functional coefficients.
method Penalized maximum likelihood estimator with adaptive LASSO penalty for simultaneous selection of spline basis functions and regressors.
result The penalized estimator outperforms the unpenalized estimator in all scenarios tested.
Hybrid model integrates GATv2 and geostatistics for better spatial prediction and uncertainty.
problem Accurate spatial prediction and uncertainty quantification in epidemiology and risk analysis.
method Integrates Graph Attention Network (GATv2) with model-based geostatistics (MBG) to capture relational and spatial dependencies.
result Hybrid model improves predictive accuracy and uncertainty quantification compared to standalone models.
Machine learning and geostatistics are powerful mathematical frameworks for modeling spatial data. Both approaches, however, suffer from poor scaling of the required computational resources for large data applications. We present the Stochastic Local Interaction (SLI) model, which employs a local representation to impr…
Proposes a transformer model with geostatistical inductive bias for spatio-temporal forecasting.
problem Combining probabilistic rigor of geostatistics with flexible deep learning representations.
method Spatially-informed transformer with learnable covariance kernel.
result Successfully recovers spatial decay parameters end-to-end via backpropagation.
New algorithm combines Geostatistics and Quantile Random Forests for non-stationary spatial modelling.
problem Non-stationary spatial modelling with multiple secondary variables.
method Combines Geostatistics and Quantile Random Forests to estimate conditional distributions and simulate spatial data.
result Consistent results similar to geostatistical and Quantile Random Forests, allowing for embedding simpler interpolation techniques.
Bayesian deep learning improves geostatistical mapping with auxiliary data.
problem Traditional geostatistical methods are limited in feature learning and uncertainty estimation.
method Deep neural networks learn complex relationships from auxiliary data for probabilistic mapping.
result Deep learning produces detailed, probabilistic maps with uncertainty estimates.
Kriging is the predominant method used for spatial prediction, but relies on the assumption that predictions are linear combinations of the observations. Kriging often also relies on additional assumptions such as normality and stationarity. We propose a more flexible spatial prediction method based on the Nearest-Neig…
Deep learning extracts terrain texture covariates for geostatistical modeling.
problem Improving prediction accuracy in geostatistical modeling using terrain texture data.
method Deep learning approach to automatically derive optimal terrain texture covariates from SRTM 90m DEM.
result Deep learning-derived covariates have strong explanatory power (R-squared around 0.6) for geochemical data.
Study compares geostatistical and machine learning models for PM2.5 prediction.
problem Improving accuracy of hourly PM2.5 maps across California.
method Traditional geostatistical methods (kriging, land use regression) and machine learning models (neural networks, random forests, support vector machines) were evaluated.
result Ensemble model enhanced predictive accuracy of PM2.5 concentration by correcting PurpleAir data bias.
A new model predicts financial volatility across firms using spatial correlations.
problem Predicting financial volatility across firms in a network.
method Heterogeneous spatiotemporal GARCH model with local likelihood estimation.
result The model captures spatial spillovers and contagion effects in financial networks.
A fundamental problem in geostatistical modeling is to infer the heterogeneous geological field based on limited measurements and some prior spatial statistics. Semantic inpainting, a technique for image processing using deep generative models, has been recently applied for this purpose, demonstrating its effectiveness…
Geostatistical learning faces unique challenges due to spatial correlation and covariate shifts.
problem Challenges in applying statistical learning to geospatial data.
method Assessing generalization error under covariate shift and spatial correlation.
result No classical learning methods are adequate for model selection in geospatial contexts.
Soil organic carbon (SOC) plays a major role in the global carbon budget. It can act as a source or a sink of atmospheric carbon, thereby possibly influencing the course of climate change. Improving the tools that model the spatial distributions of SOC stocks at national scales is a priority, both for monitoring change…
Extends geostatistical simulation method to handle multiple variables and large grids.
problem Scalability and handling of multiple variables in geostatistical simulation.
method Uses Sinkhorn optimal transport with sparse matcher and FFT-MA Gaussian backbone.
result MST-Direct reproduces joint distribution with zero histogram error and accurately preserves spatial correlation.
Direct approach for handling contextual bandits with latent state dynamics.
problem Handling contextual bandits with latent state dynamics, especially when rewards depend on posterior probabilities of hidden states.
method Direct reduction to standard linear contextual bandits, extended analysis of HMM parameters, periodic update of reward-model parameters.
result Periodic update of reward-model parameters allows handling complex dependencies in hidden states.
The calibration of a reservoir model with observed transient data of fluid pressures and rates is a key task in obtaining a predictive model of the flow and transport behaviour of the earth's subsurface. The model calibration task, commonly referred to as "history matching", can be formalised as an ill-posed inverse pr…
Efficient and high-fidelity prior sampling and inversion for complex geological media is still a largely unsolved challenge. Here, we use a deep neural network of the variational autoencoder type to construct a parametric low-dimensional base model parameterization of complex binary geological media. For inversion purp…
The present study deals with the analysis and mapping of Swiss franc interest rates. Interest rates depend on time and maturity, defining term structure of the interest rate curves (IRC). In the present study IRC are considered in a two-dimensional feature space - time and maturity. Geostatistical models and machine le…
We introduce Latent Gaussian Process Regression which is a latent variable extension allowing modelling of non-stationary multi-modal processes using GPs. The approach is built on extending the input space of a regression problem with a latent variable that is used to modulate the covariance function over the training …
New method models unknown systems with hidden parameters using neural networks.
problem Modeling unknown dynamical systems with hidden parameters.
method Training a deep neural network (DNN) model using trajectory data of the unknown system.
result DNN model accurately predicts unknown dynamical systems with new initial conditions.
Deep learning methods improve subsurface flow modeling efficiency.
problem Efficiently modeling subsurface flow with uncertain parameters.
method Two categories of deep-learning based inverse modeling methods: surrogate-based and direct.
result Deep-learning methods significantly accelerate subsurface flow modeling.
FFRK automatically extracts features for spatial interpolation without external variables.
problem Spatial interpolation challenges, especially nonstationarity and lack of explanatory variables.
method Feature-Free Regression Kriging (FFRK) method that extracts geospatial features.
result FFRK outperforms classical methods in predicting heavy metal concentrations.
Dual random fields improve mineral potential predictions.
problem Limited understanding of multi-dimensional causalities and dependencies.
method Introduces dual random fields to pool response functions across the domain.
result Spatial inference and uncertainty assessment of response models and predictions.
Learning nonlinear dynamics from diffusion data is a challenging problem since the individuals observed may be different at different time points, generally following an aggregate behaviour. Existing work cannot handle the tasks well since they model such dynamics either directly on observations or enforce the availabi…
New method for analyzing brain dynamics using HMMs and graph models.
problem Limited ability of current brain models to explain spontaneous dynamic state changes.
method Hidden Markov Graph Models (HMGMs) and spatiotemporal random walks.
result Identification of important brain community structures.
The paper builds interpretable models for property markets using machine learning.
problem Noise in real market data and differences from ideal data.
method Combining classical linear regression with kriging for land parcels, and RuleFit method for flats.
result Effective models can be built for property markets while maintaining interpretability.
New MBL hidden Born machine learns various tasks.
problem Learning from quantum many-body systems.
method MBL dynamics and hidden units for training.
result Enhanced trainability and stability in learning.
Expands Hidden Markov Model to include Markov chain observations.
problem Handling Markov chain observations in Hidden Markov Models.
method Developed Expectation-Maximization algorithm and Viterbi algorithm analogs.
result Estimates transition probabilities for hidden states and observations.
We study the computational tractability of PAC reinforcement learning with rich observations. We present new provably sample-efficient algorithms for environments with deterministic hidden state dynamics and stochastic rich observations. These methods operate in an oracle model of computation -- accessing policy and va…
Symmetry-regularized Neural ODEs improve model stability and interpretability.
problem Improving the stability and physical interpretability of Neural ODEs.
method Integrating Lie symmetries and conservation laws into the loss function.
result Symmetry-regularized Neural ODEs enhance model stability and interpretability.
DCRNN improves LSTM for chaotic dynamical system forecasting.
problem Modeling chaotic dynamical systems with recurrent neural networks.
method DCRNN incorporates learnable skip-connections and a Lyapunov stability regularization term.
result DCRNN outperforms LSTM in 100 out of 100 experiments, reducing mean squared error by 80.0%.
Investor selects portfolios based on news attention in a hidden Markov model.
problem Mean-variance portfolio selection in a dynamic attention context.
method Closed-loop equilibrium strategies via extended HJB equation and Markov chain approximation.
result Equilibrium strategies found through iterative algorithm and numerical examples.
RL agents learn from a few tasks to generalize to new ones.
problem Creating efficient RL agents that can solve multiple tasks.
method GHP-MDPs model with latent variables for hidden parameters.
result State-of-the-art performance and sample-efficiency on new tasks.
Softmax policy gradient achieves global optimality in wide neural networks with entropy regularization.
problem Optimizing softmax policies with neural networks in the mean-field regime.
method Modeling neural networks as Wasserstein gradient flows and proving global optimality of fixed points.
result Global optimality of softmax policy gradient in wide single hidden layer neural networks with entropy regularization.
Modified asymmetric hidden Markov models for time series with autoregressive components.
problem Dynamic relationships between variables in time series data.
method Introducing an asymmetric autoregressive component to recent asymmetric hidden Markov models.
result The model can choose the optimal autoregressive order for better likelihood.
CNNs predict spatial fields from sparse data.
problem Predicting complete spatial fields from limited observations.
method Convolutional Neural Networks (CNNs) trained on a single partially observed field.
result CNNs can flexibly capture local spatial patterns without explicit covariance modeling.
In this paper, we explore the effectiveness of dynamic analysis techniques for identifying malware, using Hidden Markov Models (HMMs) and Profile Hidden Markov Models (PHMMs), both trained on sequences of API calls. We contrast our results to static analysis using HMMs trained on sequences of opcodes, and show that dyn…
The paper optimizes portfolios in a market with hidden drift and random expert opinions.
problem Optimizing portfolios in a market with hidden Gaussian drift and random expert signals.
method Modeling the hidden drift using Kalman filters and solving the utility maximization problem with dynamic programming.
result Derivation of optimal portfolio weights and utility maximization under the given market conditions.
Linear Dynamical System (LDS) is an elegant mathematical framework for modeling and learning multivariate time series. However, in general, it is difficult to set the dimension of its hidden state space. A small number of hidden states may not be able to model the complexities of a time series, while a large number of …
A new theory explains large associative memory with biological plausibility.
problem Large associative memory in neurobiology and machine learning.
method Microscopic theory with hidden neurons and two-body interactions.
result Valid model of large associative memory with biological plausibility.
Purely data driven approaches for machine learning present difficulties when data is scarce relative to the complexity of the model or when the model is forced to extrapolate. On the other hand, purely mechanistic approaches need to identify and specify all the interactions in the problem at hand (which may not be feas…
Study evaluates initialization strategies for infinite hidden Markov models.
problem Limited attention to initialization in infinite hidden Markov models.
method Systematically evaluated distance-based clustering, model-based, and uniform initializations.
result Distance-based clustering initializations consistently outperform other methods.
The partially observable hidden Markov model is an extension of the hidden Markov Model in which the hidden state is conditioned on an independent Markov chain. This structure is motivated by the presence of discrete metadata, such as an event type, that may partially reveal the hidden state but itself emanates from a …
Study optimal adjustment sets for causal policies with hidden variables.
problem Estimating dynamic treatment regimes with hidden variables.
method Developed criteria for graphs without hidden variables to compare estimators, extended to dynamic policies and hidden variables.
result Existence and computation of optimal minimal and globally optimal adjustment sets.
SAGE generates subsurface velocity models from sparse well logs and seismic images.
problem Lack of high-quality subsurface velocity models due to limited data availability.
method Subsurface AI-driven geostatistical extraction using proxy posterior.
result SAGE produces geologically plausible and statistically accurate velocity realizations.
CREIMBO models diverse brain activity by identifying hidden neural sub-circuits and their non-stationary interactions.
problem Lack of alignment in neural recordings limits analysis of brain-wide dynamics.
method CREIMBO learns a unified model of neural dynamics by assuming multiple hidden global sub-circuits representing ensemble interactions.
result CREIMBO discovers session-specific neural ensembles and their non-stationary interactions, revealing cross-subject neural mechanisms.
The paper proposes a method to improve Koopman operator estimation using indicator functions.
problem Difficulty in identifying good observables for Koopman operator expansion.
method Clustering procedure based on Hidden Markov Model (HMM) to infer surrogate observables.
result Inferred indicator functions significantly improve estimation of Koopman operator eigenvalues and transition timescales.
We propose dynamical systems trees (DSTs) as a flexible class of models for describing multiple processes that interact via a hierarchy of aggregating parent chains. DSTs extend Kalman filters, hidden Markov models and nonlinear dynamical systems to an interactive group scenario. Various individual processes interact a…