Proposes a robust EM algorithm for analyzing incomplete panel count data.
problem Missing reports in panel count data.
method Functional EM algorithm for non-parametric counting process mean function estimation.
result Robust to misspecification of Poisson process assumption and missing completely at random.
We construct convergent and divergent lattices in negative curvature and give a precise asymptotic description of the behavior of their counting function.
In this article, associated with each lattice T⊆Zn the concept of a harmonic-counting measure νT on a sphere Sn−1 is introduced and it is applied to determine the asymptotic behavior of the eigenfunctions of the Laplace-Beltrami operator on a lens space. In fact, the asymptotic behavior of …
Upper bound found for Steklov eigenvalues counting function.
problem Counting Steklov eigenvalues on compact manifolds with boundary.
method Used Weyl's law and Pólya's Conjecture in the Steklov case.
result Obtained an upper bound for the counting function.
Finite precision RNNs have varying computational power, with LSTMs and ReLU-RNNs being more powerful.
problem Understanding the computational limits of finite precision RNNs for language recognition.
method Comparison of different RNN variants with finite precision and linear computation time.
result LSTMs and ReLU-RNNs are strictly stronger than other RNN variants in terms of computational power.
New test detects differences in heterogeneous datasets.
problem Detecting differences between two samples with unknown heterogeneity.
method Developed a nonparametric testing procedure that handles latent heterogeneity through a composite null.
result The test accurately detects differences in the presence of unknown heterogeneity.
This paper was motivated by work of Arnold where he explains how to count "snakes", i.e. Morse functions on the real axis with prescribed behavior at infinity. This leads immediately to a count of excellent Morse functions on the circle, where following Thom's terminology, excellent means that no two critical points li…
Anosov groups study matrix coefficients and orbit counting in symmetric spaces.
problem Anosov groups and their matrix coefficients in symmetric spaces.
method Asymptotic analysis of matrix coefficients and higher rank measures.
result Asymptotic behavior of matrix coefficients and orbit counting results.
The paper introduces a new insurance pricing model based on driving mileage.
problem Weak link between insurance premiums and mileage, leading to overdriving and accidents.
method Developed a Pay-As-You-Drive insurance pricing model using a counting process and non-homogeneous Poisson distribution.
result The model provides theoretical results for better insurance pricing based on driving behavior.
New tree-structured Markov fields with Poisson marginals for counting variables.
problem Counting variables with complex dependencies.
method Tree-structured Markov random fields with Poisson marginals.
result Straightforward sampling and joint probability calculations.
Anomaly detection in multi-modal data using cyclostationary models and neural networks.
problem Detect anomalies in multi-modal data like CCTV imagery and social media posts.
method Deep neural network for object detection, cyclostationary model for regular patterns, sequential anomaly detection algorithms.
result Asymptotically efficient anomaly detection algorithms applied to NYC 5K run detection.
Counting essential surfaces in 3-manifolds yields concise formulae and detailed asymptotics.
problem Counting isotopy classes of essential surfaces in 3-manifolds.
method Normal and almost normal surfaces, Ehrhart's lattice point counting, ideal triangulations, and new essential surface testing.
result Quasi-polynomial behavior of surface counts and concise formulae for surface numbers.
The study examines the asymptotic behavior of curve counts on surfaces.
problem Counting curves on surfaces with respect to their translation length.
method Analyzes the asymptotic behavior of curves using discrete and cocompact actions on metric spaces.
result Derives the existence of a limit for the number of curves with bounded translation length.
Non-Markovian point process shows power-law scaling, similar to nonlinear Markovian process.
problem Understanding the scaling behavior of non-Markovian point processes.
method Analyzed a confined fractional Brownian motion-driven point process and compared it to a nonlinear Markovian process.
result A nonlinear Markovian process can reproduce the power-law scaling behavior of a non-Markovian point process.
Study identifies contagion in aggregated defaults despite environmental changes.
problem Identify contagion in aggregated default counts with fluctuating probabilities.
method Compare three contagion mechanisms (Davis-Lo, Torri, Vasicek) under i.i.d. and hierarchical specifications.
result Threshold contagion is largely absorbed into environmental heterogeneity, while cumulative contagion leaves a persistent signature.
We develop an asymptotic expansion of the spectral measures on a degenerating family of hyperbolic Riemann surfaces of finite volume. As an application of our results, we study the asymptotic behavior of weighted counting functions, which, if M is compact, is defined for w≥0 and T>0 by $$N_{M,w}(T) = \sum\…
Methodology monitors processes using system call count vectors.
problem Detecting anomalies in process behavior.
method Collects system call streams, sends to server, uses ML for analysis.
result Effective in identifying process anomalies in corporate networks.
This paper introduces a novel graph-analytic approach for detecting anomalies in network flow data called GraphPrints. Building on foundational network-mining techniques, our method represents time slices of traffic as a graph, then counts graphlets -- small induced subgraphs that describe local topology. By performing…
New bounds reveal double exponential growth in conjugacy classes of fully irreducibles.
problem Counting conjugacy classes of fully irreducibles in Out(F_r).
method Equivalence to pseudo-Anosovs and logarithmic dilatations.
result Double exponential growth in the number of conjugacy classes.
This paper introduces a new task to better understand Transformers in quantitative contexts.
problem Understanding Transformers in high-stakes quantitative and scientific applications.
method Introduces a novel contextual counting task and analyzes it with causal and non-causal Transformer architectures.
result Causal attention is better suited for the contextual counting task, and no positional embeddings lead to the best accuracy.
CANN models improve insurance claim count predictions using telematics data.
problem Improving insurance claim count predictions with telematics data.
method Combining classical actuarial models with neural networks for telematics data.
result CANN models outperform traditional models in predicting insurance claims.
SessionPath improves category suggestions in type-ahead search.
problem Improving precision and recall in eCommerce type-ahead suggestions.
method SessionPath uses session embeddings and a probability distribution model to predict facets.
result SessionPath outperforms count-based and neural models in eCommerce shops.
Counting tripods on a flat torus using lattice point counting.
problem Counting finite BPS webs in flat torus geometry.
method Lattice point counting techniques in C2. result Asymptotic counting result for tripods on the torus.
Study axisymmetric σk-Nirenberg problem on spheres.
problem Prescribing σk-curvature for axisymmetric metrics on spheres. method Compactness, non-compactness, existence, and non-existence results proved based on curvature function behaviors.
result Existence and non-existence of solutions depend on curvature function behaviors near poles.
We introduce a global Cauchy-Riemann(CR)-invariant and discuss its behavior on the moduli space of CR-structures. We argue that this study is related to the Smale conjecture in 3-topology and the problem of counting complex structures. Furthermore, we propose a contact-analogue of Ray-Singer's analytic torsion. Thi…
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.
The paper develops personalized DAG models for web user behavior.
problem Understanding user behavior transitions between websites with user heterogeneity and network dependency.
method Personalized Binomial DAG models with network-structured covariates, embedding network structure into a dimension-reduced covariate, learning node neighborhoods, and exploring variance-mean relation.
result The proposed algorithm outperforms state-of-the-art competitors in heterogeneous data.
This paper investigates differentially private analysis of distance-based outliers. The problem of outlier detection is to find a small number of instances that are apparently distant from the remaining instances. On the other hand, the objective of differential privacy is to conceal presence (or absence) of any partic…
Counting orbits for Anosov groups with specific functionals.
problem Counting orbits for relatively Anosov groups with linear functionals.
method Equidistribution results and previous counting results for periods.
result Generalization of earlier work on Anosov groups.
Count-ception predicts object counts in images with reduced errors.
problem Counting objects in images is time-consuming and error-prone.
method Fully convolutional redundant counting approach using a Count-ception network.
result 20% relative improvement in accuracy over state-of-the-art methods.
It has been argued based on electric-magnetic duality and other ingredients that the Jones polynomial of a knot in three dimensions can be computed by counting the solutions of certain gauge theory equations in four dimensions. Here, we attempt to verify this directly by analyzing the equations and counting their solut…
The purpose of this article is to produce effective versions of some rigidity results in algebra and geometry. On the geometric side, we focus on the spectrum of primitive geodesic lengths (resp., complex lengths) for arithmetic hyperbolic 2-manifolds (resp., 3-manifolds). By work of Reid, this spectrum determines the …
New theorem counts curves on orbifolds.
problem Counting curves on surfaces.
method Applied Mirzakhani's theorem to orbifolds.
result Curve counting theorem extends to orbifolds.
Virtual links are generalizations of classical links that can be represented by links embedded in a ``thickened'' surface Σ×I, product of a Riemann surface of genus h with an interval. In this paper, we show that virtual alternating links and tangles are naturally associated with the 1/N2 expansion of an i…
A new method, Count-MORL, improves offline reinforcement learning by using state-action frequency.
problem Improving offline reinforcement learning performance.
method Integrates count-based conservatism into model-based offline reinforcement learning.
result The learned policy is near-optimal and outperforms existing methods.
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.
This paper announces results on the behavior of some important algebraic and topological invariants --- Euler characteristic, arithmetic genus, and their intersection homology analogues; the signature, etc. --- and their associated characteristic classes, under morphisms of projective algebraic varieties. The formulas …
Graph neural networks struggle with counting certain substructures in graphs.
problem Detecting and counting specific substructures in graphs.
method Study of graph neural networks' ability to count attributed graph substructures.
result Graph neural networks like MPNNs, 2-WL, and 2-IGNs have limitations in counting certain substructures.
Study geodesic paths on flat surfaces, comparing length and singularity counts.
problem Comparing geometric length and singularity counts on geodesic paths.
method Apply counting limit laws to infinite graphs and then to flat surfaces.
result Statistical comparison of geometric length and singularity counts on geodesic paths.
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
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.
Counts arcs in surfaces, proving convergence of geodesic currents.
problem Counting arcs of the same type in compact surfaces and related geometries.
method Derives convergence of geodesic currents to prove arc counts.
result Proves convergence of geodesic currents, leading to arc counting results.
Counted essential surfaces in a knot's exterior, finding a unique pattern.
problem Counting essential surfaces in a knot's exterior.
method Counted essential surfaces by genus, using Euler totient function. Showed normal surfaces are connected by counting their components. Used Agol, Hass, and Thurston's tools to convert component counting into orbit counting.
result Found a unique pattern in the number of essential surfaces by genus.
The abstract reviews models for analyzing count data.
problem Challenges in analyzing count data with standard methods.
method Review of generalized linear models and multinomial models.
result Fundamental connections between multinomial and count models.
Efficiently counts data streams in machine learning.
problem Counting queries in machine learning applications.
method Abstracting queries and aggregating as a stream for scalability.
result Significantly outperforms ADtrees and hash tables.
Paper proposes a method to estimate uncertainty in counting tasks in medical imaging.
problem Estimating uncertainty in counting tasks for medical imaging.
method Proposes and tests a method for calculating predictive intervals as an output of a multi-task network.
result Demonstrates the effectiveness of the technique on histopathological cell counting and white matter hyperintensity counting.
New method improves uncertainty calibration in deep learning.
problem Systematic overconfidence in EDL on out-of-distribution inputs.
method Density-Informed Pseudo-count EDL (DIP-EDL) separates class prediction from uncertainty.
result DIP-EDL achieves asymptotic concentration and enhances robustness and uncertainty calibration.
Better neural arithmetic logic units improve cell counting model generalization.
problem Neural networks struggle with high cell counts outside training data range.
method Introduced Neural Arithmetic Logic Units (NALU) for arithmetic operations in existing architectures.
result Improved cell counting accuracy for higher numeric ranges with better generalization.