New phases identified in neural scaling laws with compute limits.
problem Understanding neural scaling laws under compute constraints.
method Solved neural scaling model with stochastic gradient descent, derived loss curves, analyzed model-parameter-count phases.
result Identified 4 phases (+3 subphases) in data-complexity/target-complexity phase-plane, derived exponents.
Transformer learns to estimate negative binomial parameters efficiently.
problem Parameter estimation for over-dispersed count data in large screens.
method Pre-trained transformer trained on synthetic data generation to invert parameter to count transformation.
result Method of moments provides faster, more efficient, and better-calibrated estimates.
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 …
New insights into neural network complexity reveal better generalization performance.
problem Mysterious generalization in deep models despite high parameter counts.
method Effective dimensionality as a measure of parameter space complexity.
result Double descent behavior in generalization as a function of parameters explained.
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.
Paper proposes VAE-BPTF for better tensor factorization of sparse, imbalanced count data.
problem Inference of Bayesian Poisson-Gamma models for sparse and imbalanced count data is challenging.
method Variational auto-encoder framework with multi-layer perceptron networks for complex update information sharing and reweighting.
result VAE-BPTF outperforms current models in reconstruction errors and latent factor coherence across real-world datasets.
The study reveals a persistent bias in the distribution of holonomy on compact hyperbolic 3-manifolds.
problem The distribution of holonomy on compact hyperbolic 3-manifolds is not uniformly distributed.
method An asymptotic count of closed geodesics by their length and holonomy, and analysis of spectral parameters.
result A normalized, smoothed bias count of holonomy is distributed according to a probability distribution, controlled by the number of zero spectral parameters.
Proposes a method to handle sparse multiway count data with false zeros using zero-truncated Poisson regression.
problem Handling sparse multiway count data corrupted by false zeros.
method Zero-truncated Poisson regression with tensor completion.
result Accurate estimation of multiway count data from approximately IR2log22(I) non-zero counts. The paper models and predicts co-occurrence counts using Gamma regression.
problem Predicting relevance between items or users from high-dimensional sparse co-occurrence count data.
method Shared parameter alternating zero-inflated Gamma regression models (SA-ZIG) with Fisher scoring and learning rate adjustment.
result SA-ZIG with learning rate adjustment performs satisfactorily in predicting relevance.
Counting spheres in hyperbolic space with effective methods.
problem Counting spheres in Apollonian and Kleinian packings.
method Spectral methods and orbit counting, extending Kontorovich and Lax-Phillips techniques.
result Best-known effective error rate for sphere packing counting problems.
Generative model identifies temporal count data components with regime-dependent contributions.
problem Modeling temporal count data with regime-dependent dynamics.
method Generative framework combining regime-adaptive dynamics with Poisson log-normal emissions.
result Established identifiability of the model and revealed co-variation patterns and regime shifts.
PHIBP models complex microbiome data with shared parameters.
problem Complex, sparse count data in microbiome analysis.
method Bayesian nonparametric framework with shared species parameters.
result Flexible multivariate count model with tractable inference.
Pruning at initialization fails to find sparse subnetworks, revealing information-theoretic barriers.
problem Difficulty in finding sparse subnetworks without training the full model.
method Analysis of effective parameter count and mutual information between sparsity mask and data.
result Pruning at initialization cannot find sparse subnetworks due to high mutual information.
Capsule network (CapsNet) was introduced as an enhancement over convolutional neural networks, supplementing the latter's invariance properties with equivariance through pose estimation. CapsNet achieved a very decent performance with a shallow architecture and a significant reduction in parameters count. However, the …
Proposes PSCCA for estimating correlations and canonical correlations in sparse count data.
problem Estimating correlations and canonical correlations in sparse count data from next-generation sequencing.
method Probabilistic approach for sparse count data sets (PSCCA).
result PSCCA outperforms other methods in estimating true correlations and canonical correlations at the natural parameter level.
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.
Bayesian model fuses diverse microbiome data types.
problem Challenges in fusing different types of microbiome data.
method Flexible multinomial-Gaussian generative model with variational EM algorithm.
result Inferred latent variables provide common dimensionality reduction and predictive posterior distribution.
We consider a self-exciting counting process, the parameters of which depend on a hidden finite-state Markov chain. We derive the optimal filter and smoother for the hidden chain based on observation of the jump process. This filter is in closed form and is finite dimensional. We demonstrate the performance of this fil…
Accurate statistical models of neural spike responses can characterize the information carried by neural populations. But the limited samples of spike counts during recording usually result in model overfitting. Besides, current models assume spike counts to be Poisson-distributed, which ignores the fact that many neur…
Proposes a new DNN framework for count data with high-cardinality features.
problem Real-world data often have correlations and high-cardinality categorical features that traditional DNNs overlook.
method Introduces a hierarchical likelihood learning framework with gamma random effects for Poisson DNNs.
result Improves prediction performance by capturing nonlinear effects and subject-specific cluster effects.
Study counts rational curves on hyperKähler ALE 4-manifolds.
problem Counting rational curves on hyperKähler ALE 4-manifolds.
method Using the period map of the twistor space, count rational curves and specify complex structures.
result The integer function on the parameter space is lower semi-continuous.
We define a family of probability distributions for random count matrices with a potentially unbounded number of rows and columns. The three distributions we consider are derived from the gamma-Poisson, gamma-negative binomial, and beta-negative binomial processes. Because the models lead to closed-form Gibbs sampling …
Automatically counts microglial cells in rat spinal cord images, providing precise counts and uncertainty estimates.
problem Counting microglial cells in small, heterogeneous datasets is time-consuming and requires extensive training.
method Pre-processing to filter images, designing a non-parametric, non-linear kernel counter, providing uncertainty estimation.
result The method can provide precise counts and uncertainty estimates in small datasets, even with expert opinions.
Many popular first-order optimization methods (e.g., Momentum, AdaGrad, Adam) accelerate the convergence rate of deep learning models. However, these algorithms require auxiliary parameters, which cost additional memory proportional to the number of parameters in the model. The problem is becoming more severe as deep l…
Develops a model for RNA-seq data clustering.
problem Challenges in clustering RNA-seq count data with variable selection.
method Sparse negative binomial mixture model with lasso or fused lasso regularization.
result Superior performance in clustering accuracy, feature selection, and biological interpretation.
We introduce a new dynamical system for sequentially observed multivariate count data. This model is based on the gamma--Poisson construction---a natural choice for count data---and relies on a novel Bayesian nonparametric prior that ties and shrinks the model parameters, thus avoiding overfitting. We present an effici…
Manual count of mitotic figures, which is determined in the tumor region with the highest mitotic activity, is a key parameter of most tumor grading schemes. It can be, however, strongly dependent on the area selection due to uneven mitotic figure distribution in the tumor section.We aimed to assess the question, how s…
Efficient algorithm for graph matching in correlated stochastic block models.
problem Graph matching in correlated stochastic block models with balanced communities.
method Extends previous work on centered subgraph counts to handle estimation errors and edge correlation.
result First efficient algorithm for graph matching in the logarithmic average degree regime, matching all but a vanishing fraction of vertices with high probability.
Next-generation sequencing technologies provide a revolutionary tool for generating gene expression data. Starting with a fixed RNA sample, they construct a library of millions of differentially abundant short sequence tags or "reads", which constitute a fundamentally discrete measure of the level of gene expression. A…
The article applies Occam's Razor to non-parametric model building, minimizing the number of bits for data encoding.
problem Overlooking the role of model parameters in data encoding leads to inefficient probability density estimators.
method Extends bit counting to model parameters, providing a true measure of complexity for parametric models.
result Minimizing total bit requirement leads to smoother, more efficient probability density estimates and fewer relevant parameters.
New approach shows why overparameterized neural nets generalize well.
problem Understanding why overparameterized neural nets generalize well in practice.
method An alternative notion of capacity for attention-based models based on the effective rank of attention matrices.
result Generalization bound matches empirical scaling laws observed in large language models.
Bayesian model forecasts hospital resource use during pandemic.
problem Modeling constrained hospital resources during pandemic.
method Approximate Bayesian Computation for an ACED-HMM.
result Mechanistic approach provides competitive probabilistic forecasts.
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.
New ZIPLN model accounts for zero-inflation in multivariate count data.
problem Zero-inflation in multivariate count data.
method Introduced Zero-Inflated PLN (ZIPLN) model with variational inference.
result ZIPLN significantly improves log-likelihood and reduces dispersion.
We introduce a new sub-linear space sketch---the Weight-Median Sketch---for learning compressed linear classifiers over data streams while supporting the efficient recovery of large-magnitude weights in the model. This enables memory-limited execution of several statistical analyses over streams, including online featu…
Stochastic Kronecker graphs supply a parsimonious model for large sparse real world graphs. They can specify the distribution of a large random graph using only three or four parameters. Those parameters have however proved difficult to choose in specific applications. This article looks at method of moments estimators…
BPNNs learn to solve combinatorial problems faster and more accurately.
problem Generalizing belief propagation for efficient problem solving.
method BPNNs are parameterized operators that operate on factor graphs, generalizing BP. BPNN-D is a learned iterative operator that provably maintains BP's properties.
result BPNN-D converges 1.7x faster on Ising models and provides tighter bounds.
Transformers can store facts efficiently using associative memories.
problem Understanding how transformers store and recall factual information.
method Proved linear scaling of storage capacities for linear and MLP associative memories, introduced a synthetic task, and analyzed gradient flow.
result Shallow transformers can achieve near optimal storage capacity for factual recall tasks using associative memories.
New method constructs multi-monopoles on mapping tori.
problem Understanding wall-crossing in multi-monopole counts.
method Adiabatic limit theorem to construct multi-monopoles.
result First explicit constructions of multi-monopoles in various chambers.
New findings challenge the traditional U-shaped curve of model complexity and error, revealing a second descent in error as model size increases.
problem The traditional U-shaped curve of model complexity and prediction error is incomplete, with recent work suggesting a second descent in error as model size increases.
method Careful consideration of multiple complexity axes and a nonparametric statistics perspective were used to interpret the observed double descent curves.
result The observed double descent curves in classical statistical machine learning methods fold back into traditional convex shapes, resolving tensions with statistical intuition.
A model of random walk on knot diagrams is used to study the Alexander polynomial and the colored Jones polynomial of knots. In this context, the inverse of the Alexander polynomial of a knot plays the role of an Ihara-Selberg zeta function of a directed weighted graph, counting with weights cycles of random walk on a …
We explore the energy landscape of a simple neural network. In particular, we expand upon previous work demonstrating that the empirical complexity of fitted neural networks is vastly less than a naive parameter count would suggest and that this implicit regularization is actually beneficial for generalization from fit…
Firms miscount their customers who stop buying without saying goodbye.
problem Counting non-contractual customers accurately.
method Estimating repeat purchase probabilities and extrapolating to infinite time.
result The count of alive customers is only partially identified, with a wide range of estimates.
The seemingly disjoint problems of count and mixture modeling are united under the negative binomial (NB) process. A gamma process is employed to model the rate measure of a Poisson process, whose normalization provides a random probability measure for mixture modeling and whose marginalization leads to an NB process f…
Model analyzes cooccurrence data for recommender systems and item relevance.
problem High-dimensional cooccurrence data from online platforms.
method Shared parameter Alternating Tweedie (SA-Tweedie) model with Fisher scoring and learning rate adjustment.
result SA-Tweedie model outperforms other methods in optimizing parameters.
Researchers compute large quantum invariants for 3-manifolds.
problem Computing large values of Turaev-Viro invariants for 3-manifolds.
method Optimized backtracking algorithm, lattice point counting, preprocessing strategy, multi-precision arithmetics.
result Experimentally verified improvements over state-of-the-art implementations, supporting volume conjecture.
Study of active learning in geometric block model for community detection.
problem Active learning for community detection in geometric block model.
method Proposed two active learning algorithms combining motif-counting with label query policies.
result Sampling labels of a vanishingly small fraction of nodes is sufficient for exact recovery.
The Seiberg-Witten equation with multiple spinors generalises the classical Seiberg-Witten equation in dimension three. In contrast to the classical case, the moduli space of solutions M can be non-compact due to the appearance of so-called Fueter sections. In the absence of Fueter sections we define a sign…