RPF improves recommendation by modeling user and item interactions over time.
problem Temporal behavior and recurrent activities of users are not well modeled in existing recommendation systems.
method Introduces Recurrent Poisson Factorization (RPF) that uses a Poisson process to model temporal feedback.
result RPF outperforms state-of-the-art methods on various datasets.
This study improves fast non-Bayesian Poisson factorization for implicit-feedback recommendation systems.
problem Improving recommendation quality and speed for implicit-feedback data.
method Regularized Poisson models, frequentist optimization, sparse solutions.
result Frequentist approach yields better top-N recommendations with shorter fitting times.
NeuroMemFPP uses LSTM to estimate FPP parameters with high accuracy.
problem Estimating parameters of fractional Poisson process with memory and long-range dependence.
method Recurrent Neural Network (RNN), specifically Long Short-Term Memory (LSTM), for parameter estimation.
result The LSTM-based approach reduces MSE by about 55.3% compared to traditional MOM method.
Study shows how Poisson brackets factor on infinite dimensional manifolds.
problem Understanding Poisson brackets on infinite dimensional manifolds.
method Analyzes Poisson brackets on smoothly paracompact manifolds with specific properties.
result Dual map of a Poisson bracket factors as a smooth section of a vector bundle.
A beta-negative binomial (BNB) process is proposed, leading to a beta-gamma-Poisson process, which may be viewed as a "multi-scoop" generalization of the beta-Bernoulli process. The BNB process is augmented into a beta-gamma-gamma-Poisson hierarchical structure, and applied as a nonparametric Bayesian prior for an infi…
Study new involutivity theorems for Poisson quasi-Nijenhuis manifolds.
problem Understanding involutivity in Poisson quasi-Nijenhuis geometry.
method Present new versions of deformation and involutivity theorems under specific factorization hypotheses.
result New versions of involutivity theorems for Poisson quasi-Nijenhuis manifolds.
We develop a Bayesian Poisson matrix factorization model for forming recommendations from sparse user behavior data. These data are large user/item matrices where each user has provided feedback on only a small subset of items, either explicitly (e.g., through star ratings) or implicitly (e.g., through views or purchas…
New method for ordinal data improves recommendation systems.
problem Improving recommendation systems with ordinal data.
method Ordinal Non-negative Matrix Factorization (OrdNMF) for ordinal data.
result OrdNMF outperforms existing methods in recommendation experiments.
Framework captures missing data in sparse data sets.
problem Capturing missing data in extremely sparse data sets.
method Coupled compound Poisson factorization with stochastic variational inference.
result Explicitly modeling missing data improves results in clustering, prediction, and matrix factorization.
New insights into Gamma-Poisson model for count data.
problem Estimating topic/dictionary matrix robustness to rank over-specification.
method Rewriting GaP model free of score/activation matrix, leading to new MME algorithm.
result Automatic pruning of irrelevant dictionary columns observed empirically.
Non-negative matrix factorization models based on a hierarchical Gamma-Poisson structure capture user and item behavior effectively in extremely sparse data sets, making them the ideal choice for collaborative filtering applications. Hierarchical Poisson factorization (HPF) in particular has proved successful for scala…
Newsroom in online ecosystem is difficult to untangle. With prevalence of social media, interactions between journalists and individuals become visible, but lack of understanding to inner processing of information feedback loop in public sphere leave most journalists baffled. Can we provide an organized view to charact…
Paper introduces ZIPTF and C-ZIPTF for better tensor factorization of zero-inflated count data.
problem Inefficient tensor factorization for zero-inflated count data, especially in scRNA-seq.
method Zero Inflated Poisson Tensor Factorization (ZIPTF) and Consensus Zero Inflated Poisson Tensor Factorization (C-ZIPTF).
result ZIPTF and C-ZIPTF improve tensor factorization accuracy and consistency for zero-inflated count data.
Models for recommender systems use latent factors to explain the preferences and behaviors of users with respect to a set of items (e.g., movies, books, academic papers). Typically, the latent factors are assumed to be static and, given these factors, the observed preferences and behaviors of users are assumed to be ge…
Flexible models cluster RNA sequencing data.
problem Clustering discrete data from RNA sequencing studies.
method Finite mixtures of multivariate Poisson-log normal factor analyzers with constraints.
result Models give favorable clustering performance on real and simulated data.
We present a Bayesian tensor factorization model for inferring latent group structures from dynamic pairwise interaction patterns. For decades, political scientists have collected and analyzed records of the form "country i took action a toward country j at time t"---known as dyadic events---in order to form an…
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 …
Graph morphism maps Poisson cocycles to symmetries, revealing factorization through Jacobi identity.
problem Mapping graph cocycles to symmetries of Poisson structures.
method Kontsevich graph orientation morphism and differential consequences of Jacobi identity.
result Existence of factorization through differential consequences of Jacobi identity.
This paper uses cPF to build recommender systems from raw count data.
problem Sparse, over-dispersed and bursty count data make direct use in recommender systems challenging.
method Compound Poisson Factorization (cPF) with a unified framework (dcPF) and adaptive algorithm.
result dcPF achieves better recommendation scores than Poisson Factorization on raw or binarized data.
Model-based collaborative filtering analyzes user-item interactions to infer latent factors that represent user preferences and item characteristics in order to predict future interactions. Most collaborative filtering algorithms assume that these latent factors are static, although it has been shown that user preferen…
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.
RVRAE combines deep learning and dynamic factor models for better stock returns prediction.
problem Improving stock returns prediction in volatile markets.
method Combines dynamic factor modeling with variational recurrent autoencoder (VRAE). Uses prior-posterior learning for optimal factor model.
result RVRAE outperforms traditional methods in predicting stock returns and estimating variances.
This paper develops a spectral theory of Markovian asset pricing models where the underlying economic uncertainty follows a continuous-time Markov process X with a general state space (Borel right process (BRP)) and the stochastic discount factor (SDF) is a positive semimartingale multiplicative functional of X. A key …
Proposes a deep learning model to improve stock market prediction.
problem Lack of interpretability in linear multi-factor models for stock prediction.
method Extends linear multi-factor model to LSTM+LRP for non-linear and time-varying predictions.
result Deep recurrent factor model outperforms traditional models in predictive capability.
To infer a multilayer representation of high-dimensional count vectors, we propose the Poisson gamma belief network (PGBN) that factorizes each of its layers into the product of a connection weight matrix and the nonnegative real hidden units of the next layer. The PGBN's hidden layers are jointly trained with an upwar…
New method compresses neural networks up to 14x with minimal performance loss.
problem Compressing neural networks for real-time applications.
method Post-training rank-selection method called Rank-Tuning.
result High compression rates with minimal performance degradation.
Study Poisson structures on fibered 5-manifolds with compatibility conditions.
problem Understanding Poisson structures on fibered 5-manifolds.
method Using almost coupling condition and bigraded factorization of the Jacobi identity.
result Describe global behavior and singularities of almost coupling Poisson tensors.
Let X be a simply connected compact Riemannian symmetric space, let U be the universal covering group of the identity component of the isometry group of X, and let \g denote the complexification of the Lie algebra of U, \g=\u^\C. Each \u-compatible triangular decomposition \g=\n_- + \h + \n_+ determines a Poisson Lie g…
Enhances count process modelling with Markov-modulated non-homogeneous Poisson process.
problem Count data modelling challenges, especially in complex scenarios.
method Introduces a flexible frequency perturbation measure into Markov-modulated Poisson process framework.
result Natural incorporation of observed event arrivals and latent factors.
KF-RTRL approximates RTRL for online learning of long-term dependencies.
problem Lack of efficient algorithms for learning long-term dependencies in RNNs.
method KF-RTRL uses Kronecker factorization to approximate RTRL gradients.
result KF-RTRL is an unbiased, memory-efficient online learning algorithm with lower noise than UORO.
The paper studies quasi-Sturmian colorings on regular trees, distinguishing bounded and unbounded types.
problem Coloring regular trees with quasi-Sturmian properties.
method Developed an induction algorithm similar to Sturmian colorings, distinguishing types by recurrence function.
result Obtained an induction algorithm for quasi-Sturmian colorings on regular trees.
New algorithm guarantees optimal convergence rate for stochastic optimization.
problem Optimal convergence rate for stochastic optimization algorithms.
method Regularized versions of Minimization by Incremental Surrogate Optimization (MISO) with arbitrary recurrent data sampling.
result Expected optimality gap converges at O(n−1/2) under general recurrent sampling schemes. Paper uses neural networks to detect anomalies in graph time series data.
problem Anomaly detection on graph time series data.
method Combines RNN, VI, and graph convolutional network for anomaly detection.
result Demonstrates improved anomaly detection capability on traffic flow data.
Recurrent iterated function systems (RIFSs) are improvements of iterated function systems (IFSs) using elements of the theory of Marcovian stochastic processes which can produce more natural looking images. We construct new RIFSs consisting substantially of a vertical contraction factor function and nonlinear transform…
RIMs improve generalization by specializing modular structures.
problem Improving generalization and robustness to changes in tasks.
method Recurrent Independent Mechanisms (RIMs) architecture with independent dynamics, sparing communication, and selective updates.
result RIMs lead to dramatic improvement in generalization on tasks with varying factors.
The paper explains practical insights for sparse network modeling.
problem Resolving pathologies in traditional network modeling, focusing on sparsity.
method Sparse exchangeable graphs, network subsampling, test-train dataset splitting, mean field variational inference.
result Practical insights and methods for sparse network modeling.
The paper develops new inequalities for Markov chain sums, linking them to mixing time.
problem Establishing concentration inequalities for Markov chain sums.
method Developed novel concentration inequalities for geometrically ergodic Markov chains, linking bounds to mixing time constants.
result Explicit bounds for additive functionals of Markov chains, linked to Rosenthal inequality constants and mixing properties.
Bayesian hierarchical tensor factorization model for international trade flows
problem Sparse semi-continuous tensor data modeling
method Bayesian hierarchical tensor factorization with Poisson and Gamma models
result Identifies multiway dependence in trade flows
A method to construct fractal surfaces by recurrent fractal curves is provided. First we construct fractal interpolation curves using a recurrent iterated functions system(RIFS) with function scaling factors and estimate their box-counting dimension. Then we present a method of construction of wider class of fractal su…
New model handles uneven time intervals better than traditional methods.
problem Irregularly-sampled time series data.
method Generalizes RNNs to ODE-RNNs, explicitly modeling observation gaps.
result ODE-RNNs outperform traditional models on irregular data.
The paper shows deep connections between exotic smoothings of a small R^4 (the spacetime), the leaf space of codimension-1 foliations (related to noncommutative algebras) and quantization. At first we relate a small exotic R^4 to codimension-1 foliations of the 3-sphere unique up to foliated cobordisms and characterize…
Topic-aware chatbot learns from NMF topic vectors.
problem Improving chatbot relevance based on user topics.
method Combines RNN with NMF for topic learning and attention.
result Chatbot provides more relevant answers based on topic.
A common approach to analyze a covariate-sample count matrix, an element of which represents how many times a covariate appears in a sample, is to factorize it under the Poisson likelihood. We show its limitation in capturing the tendency for a covariate present in a sample to both repeat itself and excite related ones…
We outline the notions and concepts of the calculus of variational multivectors within the Poisson formalism over the spaces of infinite jets of mappings from commutative (non)graded smooth manifolds to the factors of noncommutative associative algebras over the equivalence under cyclic permutations of the letters in t…
Paper introduces a new model for polyphonic music composition.
problem Creating music with multiple interwoven voices.
method Developed a coupled recurrent model using probabilistic factorization and neural network ideas.
result Trained models for single-voice and multi-voice composition on a large dataset.
A new model BGAR(1) improves temporal NMF for time series data.
problem Temporal NMF models lack a well-defined stationary distribution.
method Introduced a new Gamma Markov chain model BGAR(1) to overcome the limitation of previous models.
result BGAR(1) model has a well-defined stationary distribution.
Optimizes Bayesian priors for matrix factorization without posterior inference.
problem Selecting optimal priors for Bayesian models in machine learning.
method Prior predictive distribution and virtual statistics matching user-provided or observed data statistics.
result Analytically determines hyperparameters for Poisson factorization models.
A new deep approach to Kalman filtering integrates uncertainty estimates efficiently.
problem Integrating uncertainty estimates into deep time-series models.
method Proposes a Recurrent Kalman Network (RKN) that learns directly using backpropagation.
result RKN obtains more accurate uncertainty estimates and slightly improved prediction performance.