New framework models graph signals as distribution-valued signals in Wasserstein space.
problem Limitations of classical vector-based GSP, including synchronous observations and uncertainty.
method Introduces graph distribution-valued signals (GDSs) in the Wasserstein space.
result GDSs naturally encode uncertainty and stochasticity, generalizing traditional graph signals.
Wasserstein gradient boosting predicts probability distributions for supervised learning.
problem Distribution-valued supervised learning where outputs are probability distributions.
method Fits a new weak learner to Wasserstein gradients of loss functionals of probability distributions.
result Superior performance in probabilistic prediction compared to existing methods.
We will study metric measure spaces (X,d,m) beyond the scope of spaces with synthetic lower Ricci bounds. In particular, we introduce distribution-valued lower Ricci bounds BE1(κ,∞) ∙ for which we prove the equivalence with sharp gradient estimates, ∙ the class of which will be preserved under…
CAST predicts distribution-valued time series by stabilizing and transporting simplex-supported successors.
problem Forecasting distribution-valued time series with structural failure modes.
method CAST (Causal Anchored Simplex Transport) uses successors retrieved from causal context, stabilized with a persistence anchor, and locally transported on ordered supports.
result CAST outperforms baselines on eleven public and simulated benchmarks, achieving best average rank on both one-step KL and autoregressive rollout JSD.
Price movements of stock market are not totally random. In fact, what drives the financial market and what pattern financial time series follows have long been the interest that attracts economists, mathematicians and most recently computer scientists [17]. This paper gives an idea about the trend analysis of stock mar…
Enhances financial market valuation and trading algorithms using distributional value functions.
problem Accurate valuation and optimal trading decisions in financial markets.
method Combines predictive knowledge and deep reinforcement learning to introduce CDG-Model, a flexible framework for financial market valuation and trading.
result Improved market valuation and trading performance through enhanced feature creation and integration of real-world market factors.
Distributional (or distribution-valued) data are a new type of data arising from several sources and are considered as realizations of distributional variables. A new set of fuzzy c-means algorithms for data described by distributional variables is proposed. The algorithms use the L2 Wasserstein distance between dist…
We show injectivity of the X-ray transform and the d-plane Radon transform for distributions on the n-torus, lowering the regularity assumption in the recent work by Abouelaz and Rouvière. We also show solenoidal injectivity of the X-ray transform on the n-torus for tensor fields of any order, allowing the tensor…
This paper improves credit line impact analysis by considering spending as a distribution.
problem Previous studies on credit lines' impact on spending have overlooked the distributional nature of spending.
method Developed a distribution-valued estimator framework to extend existing real-valued estimators.
result Credit lines positively influence spending across all quantiles, but more towards luxuries as they increase.
Novel framework for quantifying data distribution values.
problem Quantifying the value of data distributions from samples.
method Generalized Bayesian Inference with loss from transferability measures.
result Unified solution for various practical problems.
The paper analyzes the risk of investing in a basket of 27 cryptocurrencies using statistical distributions.
problem Risk assessment of capital allocation in a basket of cryptocurrencies.
method Used statistical tests to determine the most appropriate distribution (SDI) for modeling returns, and adapted the generalized Pareto distribution for tail risk assessment.
result Found that a combination of stable and generalized Pareto distributions provides a more accurate risk assessment for the basket of cryptocurrencies.
Optimizes option portfolios for skewed-t returns using VaR and variance measures.
problem Optimizing portfolios for skewed-t returns with heavy tails and skewness.
method Uses variance and VaR measures, departing from normal returns, and provides explicit portfolio weights.
result Optimal portfolio weights differ significantly from variance optimal weights due to skewness.
New method explains anomalies in multivariate time series data.
problem Understanding and explaining anomalies in multivariate time series data.
method Counterfactual reasoning applied to MDI-detected anomalous intervals.
result Our method accurately identifies and explains anomalies in various extreme events.
Spaces of convex and concave functions appear naturally in theory and applications. For example, convex regression and log-concave density estimation are important topics in nonparametric statistics. In stochastic portfolio theory, concave functions on the unit simplex measure the concentration of capital, and their gr…
Estimates low-rank distributional matrices from incomplete samples.
problem Matrix completion for distributional entries with limited observed data.
method Kernel mean embeddings, Tucker rank, functional unfolding operators.
result Effective estimator for distributional matrix completion established.
Deep neural networks forecast financial return distributions accurately.
problem Forecasting probability distributions of financial returns.
method Used 1D CNN and LSTM architectures with custom loss functions to optimize distribution parameters.
result LSTM with skewed Student's t distribution outperformed classical models in multiple evaluation metrics.
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.
Schrödinger bridge solved with Weyl calculus for quadratic state cost.
problem Optimal control policy to steer joint state statistics.
method Weyl calculus in quantum mechanics for reaction-diffusion PDEs.
result Explicit Markov kernel for quadratic state cost found.
Wasserstein Policy Learning for Distributional Outcomes
problem Offline policy learning with distribution-valued outcomes
method Establishing statistical guarantees for policy learning framework
result Proven leading dependence on N and N-dim(Π) for finite-sample regret
Paper develops privacy-preserving mechanisms for machine learning using wavelet transforms.
problem Improper data privacy methods compromise user data even with small preliminary knowledge.
method Three privacy-preserving mechanisms with discrete M-band wavelet transform.
result Successfully retains both differential privacy and learnability in various machine learning environments.
New method predicts spatial events like hurricanes and earthquakes with uncertainty.
problem Quantifying uncertainty in natural hazard predictions.
method Representing spatial point clouds as empirical measures, constraining prediction sets to spatial data manifold, using Wasserstein distance.
result Achieves near-nominal coverage and lower energy/manifold distances compared to baselines.
New method for multivariate distribution regression using NPT metric.
problem Regression with multivariate distributional responses and Euclidean predictors.
method Fréchet regression with nonparanormal transport (NPT) metric.
result Efficient estimation and granular interpretation of predictor effects.
ARL bridges non-Markovian decision processes with reinforcement learning, improving foresight and stability.
problem Inaccurate foresight in non-Markovian environments due to state-based methods' limitations.
method Lifted state space into a signature-augmented manifold, using a self-consistent field approach to anticipate future path-law.
result ARL achieves deterministic evaluation of expected returns with reduced computational complexity and variance.
QR-MIX models joint state-action values as a distribution to handle randomness in MARL.
problem Randomness in rewards and observations leads to randomness in long-term returns in MARL.
method QR-MIX uses quantile regression and combines it with QMIX and IQN to model joint state-action values as a distribution.
result QR-MIX outperforms QMIX in the StarCraft Multi-Agent Challenge (SMAC) environment.
In situations like tax declarations or analyzes of household budgets we would like to automatically evaluate credibility of exogenous variable (declared income) based on some available (endogenous) variables - we want to build a model and train it on provided data sample to predict (conditional) probability distributio…
Symbolic data analysis (SDA) is an emerging area of statistics concerned with understanding and modelling data that takes distributional form (i.e. symbols), such as random lists, intervals and histograms. It was developed under the premise that the statistical unit of interest is the symbol, and that inference is requ…
DFR models dynamic distributional data with weighted Fréchet means.
problem Regression of distribution-valued responses over time.
method Dynamic Fréchet Regression (DFR) with index-aware weighting and feature selection.
result Improved predictive accuracy and feature recovery over existing methods.
New algorithms for collaborative reinforcement learning with limited communication.
problem Efficiently learning value functions in multi-agent systems with strict information constraints.
method Distributed gradient-based temporal difference algorithms with consensus schemes.
result Parameter estimates converge to ODEs with defined invariant sets under general assumptions.
A new geometry for comparing signals, overcoming traditional limitations.
problem Comparing and interpolating discontinuous and signed signals.
method Investigation of Riemannian geometry on signal space, introducing a metric that measures both horizontal and vertical deformations.
result Characterization of metric properties and establishment of geodesic regularity and stability.
Paper presents a unique method to recover signals from their bispectrum.
problem Retrieving signals accurately from their bispectrum.
method Two-step trust region algorithm that minimizes a non-convex objective function.
result Signals with finite spectral or temporal support can be recovered from at least 3B measurements of their bispectrum.
Paper proposes efficient methods for clustering and signal recovery in high-dimensional data with block structures.
problem High-dimensional clustering and signal recovery under block signal structures.
method CFA-PCA and MA-PCA methods for sparse and dense block signals.
result Proposed methods achieve computational minimax optimality for clustering and signal recovery.
Proposes a novel graph signal model using narrowband kernels.
problem Graph signals with multiple concentrated frequency regions.
method Jointly learns graph signal model parameters and coefficients.
result Joint learning improves signal interpolation accuracy.
New algorithms improve signal processing in federated learning.
problem Efficiently process distributed signal samples with privacy and communication constraints.
method Proposes overpredictive signal approximations using convex optimization.
result Quantifies tradeoffs between communication cost, sampling rate, and approximation error.
We consider the problem of signal recovery on graphs as graphs model data with complex structure as signals on a graph. Graph signal recovery implies recovery of one or multiple smooth graph signals from noisy, corrupted, or incomplete measurements. We propose a graph signal model and formulate signal recovery as a cor…
Proposes a new signal model for high-dimensional, small-sample-size data.
problem Signal detection in high-dimensional, small-sample-size datasets.
method Intrinsic signal model based on dynamical system assumption.
result Taguchi method effectively detects signals in the proposed model.
This paper reconstructs complex graph signals using kernel methods on manifolds.
problem Reconstructing complex graph signals from samples on graph vertices.
method Kernel methods on complex manifolds, embedding vertices into higher-dimensional spaces.
result Effective reconstruction of complex graph signals, outperforming conventional methods.
Study on signal-plus-noise decomposition in nonlinear spiked random matrices.
problem Nonlinear spiked random matrix models with rank-one signal and noise.
method Signal-plus-noise decomposition and phase transition analysis.
result Identified precise phase transitions in signal components at critical thresholds.
We find ways to make physical signals misclassified by computer vision models.
problem Vulnerability of signal classifiers to adversarial perturbations in physical signals.
method Solving PDE-constrained optimization problems to construct imperceptible perturbations.
result Effective and physically realizable adversarial perturbations can be computed for machine learning models.
The presence of noise is common in signal processing regardless the signal type. Deep neural networks have shown good performance in noise removal, especially on the image domain. In this work, we consider deep neural networks as a denoising tool where our focus is on one dimensional signals. We introduce an encoder-de…
In this paper, we address the problem of reconstructing a time-domain signal (or a phase spectrogram) solely from a magnitude spectrogram. Since magnitude spectrograms do not contain phase information, we must restore or infer phase information to reconstruct a time-domain signal. One widely used approach for dealing w…
Optimizes signal detection in particle physics by decorrelating classifiers.
problem Systematic errors in background models can mislead signal detection.
method Use optimal transport to decorrelate classifiers from protected variables, then apply semiparametric mixture model.
result Decorrelation and signal enrichment improve the stability, robustness, and power of signal detection tests.
Signal recovery is one of the key techniques of Compressive sensing (CS). It reconstructs the original signal from the linear sub-Nyquist measurements. Classical methods exploit the sparsity in one domain to formulate the L0 norm optimization. Recent investigation shows that some signals are sparse in multiple domains.…
Paper improves signal proportion estimation by accounting for variable dependence.
problem Traditional estimators assume independence, limiting applicability in real-world scenarios.
method Integrates arbitrary covariance dependence information using principal factor approximation.
result Method outperforms state-of-the-art estimators in accuracy and detection of weaker signals.
Signal retrieval from a series of indirect measurements is a common task in many imaging, metrology and characterization platforms in science and engineering. Because most of the indirect measurement processes are well-described by physical models, signal retrieval can be solved with an iterative optimization that enfo…
Goal: This paper deals with the problems that some EEG signals have no good sparse representation and single channel processing is not computationally efficient in compressed sensing of multi-channel EEG signals. Methods: An optimization model with L0 norm and Schatten-0 norm is proposed to enforce cosparsity and low r…
A new model classifies lightning signals more accurately across different scales.
problem Classifying VLF lightning transients to reduce interference and improve navigation system reliability.
method Introduces a multi-scale residual transformer (MRTransformer) to classify lightning signals.
result Achieved 90% accuracy in lightning signal classification.
Generalizes PCA and ICA for continuous-time signals using neural networks.
problem Low-rank decomposition of continuous-time vector-valued signals.
method Implicit neural network framework to learn numerical approximations of PCA and ICA.
result Unified approach to PCA and ICA in continuous domain, enforcing decorrelation and independence.
Research compares ML and Time Series methods for generating trading signals.
problem Efficiency of on-line learning Algorithms in generating trading signals.
method Used technical indicators and ensemble of Random Forests, also Kalman Filter.
result Kalman Filter outperformed Random Forests in on-line learning predictions of stock prices.