Proposes a method to reconcile count time series forecasts.
problem No formal framework for probabilistic reconciliation of count time series.
method Generalizes Bayes' rule for reconciling real-valued and count variables.
result Improves forecast accuracy for count variables compared to Gaussian reconciliation.
Time series of counts arise in a variety of forecasting applications, for which traditional models are generally inappropriate. This paper introduces a hierarchical Bayesian formulation applicable to count time series that can easily account for explanatory variables and share statistical strength across groups of rela…
Warped DLMs improve forecasting for count time series.
problem Limited options for modeling count time series data.
method Introduces a semiparametric methodology using warping of Gaussian DLMs.
result Demonstrates improved forecasting capabilities for count time series.
We tackle anomaly detection in sparse time series data.
problem Sparse time series with low signal-to-noise ratios and non-uniform performance.
method We introduce a novel generative procedure for benchmark datasets and demonstrate how anomaly score smoothing improves performance.
result Anomaly score smoothing consistently improves performance in low-count time series anomaly detection.
The paper introduces neural INGARCH models for time series of counts.
problem Analyzing time series of counts using traditional INGARCH models.
method Combining artificial neural networks with INGARCH models.
result Neural INGARCH models outperform traditional models in information loss.
Graphical estimation of count time series dependencies.
problem Estimating dependencies between multivariate count time series.
method Parameter-driven generalized linear model with l1-type regularization and MCEM algorithm.
result Characterization of disease spread interdependence and sources/sinks in Greater Mumbai.
Proposes a new model to better handle overdispersed count time series.
problem Heterogeneous overdispersed count time series.
method Negative-Binomial Randomized Gamma Markov Process.
result Significantly improves predictive performance and fast convergence of inference algorithm.
New exact tests detect changepoints in binary and count data, especially when normal approximations fail.
problem Detecting changepoints in multichannel binary and count data.
method Exact tests combining two-sample conditional tests with multiplicity correction.
result Exact tests are much more powerful than asymptotic tests in various settings.
Study on counting orbits and Poincaré series for specific hyperbolic metrics.
problem Counting orbits and analyzing Poincaré series for strongly hyperbolic metrics.
method Combining ergodic theory techniques with topological flows and symbolic dynamics.
result Obtained orbital counting results and described the domain of analyticity for Poincaré series.
The Poincaré series for surfaces with boundary extends to the complex plane.
problem Counting geodesics on surfaces with boundaries.
method Analytic continuation of Poincaré series.
result Poincaré series extend meromorphically to the whole complex plane.
The paper proposes count echo state networks for forecasting graduate student enrollments.
problem Forecasting graduate student enrollments from historical data.
method Developed hierarchical count echo state networks and compared them to Poisson autoregressions and negative binomial models.
result Hierarchical negative binomial based echo state network is the superior model.
Proposes a new distribution for robust time series modeling with heavy tails.
problem Robust modeling of time series with heavy-tailed noise.
method Spliced Binned-Pareto distribution for non-stationary time series.
result Accurately models extreme events and captures time dependencies in higher moments.
CMoS improves time series forecasting with minimal parameters.
problem Efficiently forecasting time series data with limited resources.
method CMoS directly models chunk-wise spatial correlations, using Correlation Mixing and Periodicity Injection techniques.
result CMoS outperforms state-of-the-art models with minimal parameters.
The study uses Gaussian Processes with Tweedie likelihood for forecasting intermittent time series.
problem Forecasting intermittent time series with high accuracy and flexibility.
method The approach combines Gaussian Processes with two forecast distributions: negative binomial and Tweedie.
result TweedieGP provides better probabilistic forecasts, especially for high quantiles.
We study the counting function of topological Poincaré series associated with rational homology sphere plumbed 3-manifold with connected negative definite tree, interpreting as an alternating sum of coefficient functions associated with some Taylor expansions. It is motivated by a theorem of Szenes and Vergne which exp…
Proposes a new algorithm for efficient probabilistic reconciliation of forecasts.
problem Ensuring coherence in forecasts for hierarchical time series.
method Bottom-Up Importance Sampling algorithm for any type of forecast distribution.
result Significant improvement over base probabilistic forecasts in experiments.
TimeCNN improves forecasting by refining cross-variable interactions over time.
problem Multivariate time series forecasting struggles with dynamic and multifaceted cross-variable correlations.
method TimeCNN uses timepoint-independent convolution kernels to capture evolving relationships among variables.
result TimeCNN outperforms state-of-the-art models in real-world datasets with significant computational and speed advantages.
We develop deep Poisson-gamma dynamical systems (DPGDS) to model sequentially observed multivariate count data, improving previously proposed models by not only mining deep hierarchical latent structure from the data, but also capturing both first-order and long-range temporal dependencies. Using sophisticated but simp…
The involutory birack counting invariant is an integer-valued invariant of unoriented tangles defined by counting homomorphisms from the fundamental involutory birack of the tangle to a finite involutory birack over a set of framings modulo the birack rank of the labeling birack. In this first of an anticipated series …
Novel model for predicting event intensities from static and time series data.
problem Predicting event intensities from static and irregularly sampled time series data.
method Neural controlled differential equations and signature-based CoxSig model.
result The CoxSig model provides theoretical learning guarantees and performs well on various datasets.
Paper compares neural networks and time-series models for weather derivative pricing.
problem Pricing accuracy and regime adaptation for temperature and precipitation weather derivatives.
method Benchmarked harmonic-regression/ARMA vs. feed-forward neural network for temperature. Used CNN for precipitation, adapting to seasonal heterogeneity.
result CNN yields more accurate pricing, especially for regime-adapted seasonal data.
New algorithms improve time series prediction with uncertainty quantification.
problem Uncertainty quantification for time series prediction.
method Combines conformal prediction and control theory for online, adaptive forecasting.
result Improves coverage over ensemble forecasters in real-world applications.
Study examines how different time series cross-validation methods affect anomaly detection in multivariate time series.
problem Evaluating anomaly detection in multivariate time series requires preserving temporal dependencies, especially for subsequence anomalies.
method Systematically investigates walk-forward and sliding window methods across various validation configurations and classifier types.
result Sliding window method consistently yields higher precision-recall scores and reduced fold-to-fold performance variance, particularly for deep learning models.
Bayesian models forecast COVID-19 hospitalizations at single sites.
problem Forecasting daily COVID-19 hospitalizations at a single hospital.
method Hierarchical Bayesian models with generalized Poisson likelihood and autoregressive/Gaussian process latent processes.
result Demonstrated superior performance compared to baselines in public datasets.
We discuss relations between quantum BPS invariants defined in terms of a product decomposition of certain series, and difference equations (quantum A-polynomials) that annihilate such series. We construct combinatorial models whose structure is encoded in the form of such difference equations, and whose generating fun…
We introduce an algorithm for the segmentation of a class of regime switching processes. The segmentation algorithm is a non parametric statistical method able to identify the regimes (patches) of the time series. The process is composed of consecutive patches of variable length, each patch being described by a station…
\textit{SummerTime} seeks to summarize globally time series signals and provides a fixed-length, robust summarization of the variable-length time series. Many classical machine learning methods for classification and regression depend on data instances with a fixed number of features. As a result, those methods cannot …
Detailed study of multifractal characteristics of the financial time series of asset values and of its returns is performed using a collection of the high frequency Deutsche Aktienindex data. The tail index (α), the Renyi exponents based on the box counting algorithm for the graph (dq) and the generalized Hurst ex…
FreDN separates trends and periodicities in non-stationary time series forecasts.
problem Spectral entanglement and computational burden in frequency-domain methods for non-stationary time series.
method FreDN introduces a learnable Frequency Disentangler module to separate trend and periodic components directly in the frequency domain, and uses a ReIm Block to reduce complexity.
result FreDN outperforms state-of-the-art methods by up to 10% on long-term forecasting benchmarks.
FOCUS method forecasts counterfactuals in panel data with time series dynamics.
problem Forecasting unobserved potential outcomes in causal inference with missing entries and latent factors.
method FOCUS extends matrix completion methods by leveraging time series dynamics of latent factors.
result FOCUS method outperforms existing benchmarks in predicting future counterfactuals.
Neural networks parameterize time-varying Markov dynamics in financial time series.
problem Estimating Markov transition matrices in high-resolution, high-noise financial data.
method Introduces a neural network framework to generate explicit, time-varying Markov transition matrices, constraining neural outputs to formal stochastic operators.
result Learned operators capture regime shifts, with high-volatility regimes homogenizing transition dynamics.
GGP models multivariate time series with latent sub-sequences for diverse behaviors.
problem Modeling multivariate time series with diverse behaviors and patterns.
method Graph Gamma Process (GGP) linear dynamical systems with latent sub-sequences.
result GGP models exhibit good predictive performance and reveal interpretable latent patterns.
Paper connects knot invariants and Morse flow loops.
problem Connecting quantum group invariants and Morse flow loops for knot study.
method Defining a two-variable series invariant by counting Morse flow loops in knot complements and proving it agrees with quantum group BPS series.
result Correspondence proven for all braid-homogeneous knots.
Flow Matching for count data improves sample quality and efficiency.
problem Mapping between count distributions across batches or time points in high-dimensional count data.
method count-FM, a flow-matching framework based on a continuous-time birth-death process with local unit jumps.
result count-FM achieves better sample quality than representative baselines while using fewer parameters.
Study uses regression and ML for COVID-19 mortality forecasting.
problem Forecasting COVID-19 mortality during the first wave in Spain.
method Cyclical curve log-regression, multivariate time series spatial residual correlation analysis, Bayesian approach, machine learning.
result Empirical analysis shows ML regression models perform better than traditional methods.
Polynomial-time methods count and sample DAGs from equivalence classes.
problem Counting and sampling DAGs from Markov equivalence classes.
method Polynomial-time algorithms for DAGs.
result Counting and sampling can be done in polynomial time.
Counting objects in digital images is a process that should be replaced by machines. This tedious task is time consuming and prone to errors due to fatigue of human annotators. The goal is to have a system that takes as input an image and returns a count of the objects inside and justification for the prediction in the…
This note addresses some questions that arise in the series of works by Kyoji Saito on the growth functions of graphs. We study "hyperbolike" graphs, which include Cayley graphs of hyperbolic groups. We generalize some well-known results on hyperbolic groups to the hyperbolike setting, including rationality of generati…
A gamma process dynamic Poisson factor analysis model is proposed to factorize a dynamic count matrix, whose columns are sequentially observed count vectors. The model builds a novel Markov chain that sends the latent gamma random variables at time (t−1) as the shape parameters of those at time t, which are linked …
The study focuses on estimating and predicting time-varying origin to destination (OD) trip tables for a dynamic traffic assignment (DTA) model. A bi-level optimisation problem is formulated and solved to estimate OD flows from pre-existent demand matrix and historical traffic flow counts. The estimated demand is then …
The statistical properties of the bid-ask spread of a frequently traded Chinese stock listed on the Shenzhen Stock Exchange are investigated using the limit-order book data. Three different definitions of spread are considered based on the time right before transactions, the time whenever the highest buying price or th…
We consider vector fields X on a closed manifold M with rest points of Morse type. For such vector fields we define the property of exponential growth. A cohomology class ξ∈H1(M;R) which is Lyapunov for X defines counting functions for isolated instantons and closed trajectories. If X has exponent…
In this paper, we study a new graph learning problem: learning to count subgraph isomorphisms. Different from other traditional graph learning problems such as node classification and link prediction, subgraph isomorphism counting is NP-complete and requires more global inference to oversee the whole graph. To make it …
Polynomial-time methods count and sample DAGs from Markov classes.
problem Counting and sampling Markov equivalent DAGs.
method Polynomial-time algorithms for DAGs from Markov classes.
result Long-standing open problem solved, making practical infeasible strategies feasible.
Deviance-style normalization for sparse, jointly overdispersed count matrices
problem Jointly overdispersed count matrices
method Dirichlet-multinomial deviance residualization
result Preserves exact sparsity, evaluates in constant time, recovers multinomial residual
We present the first framework for Gaussian-process-modulated Poisson processes when the temporal data appear in the form of panel counts. Panel count data frequently arise when experimental subjects are observed only at discrete time points and only the numbers of occurrences of the events between subsequent observati…
The study counts Salem numbers linked to arithmetic hyperbolic orbifolds.
problem Bounding the proportion of Salem numbers in arithmetic lattices.
method Using results on the distribution of Salem numbers, classical methods for counting Pythagorean triples, and Gauss' lattice-counting argument.
result Improved bounds on the proportion of Salem numbers and strong exponential growth of averages.
p-SNE embeds Poisson count data into low dimensions preserving structure.
problem Embedding high-dimensional sparse Poisson data into a low-dimensional space.
method p-SNE (Poisson Stochastic Neighbor Embedding) using KL divergence and Hellinger distance.
result p-SNE recovers meaningful structure in real-world count datasets.