2,392 research outputs found
Scalable Bayesian Non-Negative Tensor Factorization for Massive Count Data
We present a Bayesian non-negative tensor factorization model for
count-valued tensor data, and develop scalable inference algorithms (both batch
and online) for dealing with massive tensors. Our generative model can handle
overdispersed counts as well as infer the rank of the decomposition. Moreover,
leveraging a reparameterization of the Poisson distribution as a multinomial
facilitates conjugacy in the model and enables simple and efficient Gibbs
sampling and variational Bayes (VB) inference updates, with a computational
cost that only depends on the number of nonzeros in the tensor. The model also
provides a nice interpretability for the factors; in our model, each factor
corresponds to a "topic". We develop a set of online inference algorithms that
allow further scaling up the model to massive tensors, for which batch
inference methods may be infeasible. We apply our framework on diverse
real-world applications, such as \emph{multiway} topic modeling on a scientific
publications database, analyzing a political science data set, and analyzing a
massive household transactions data set.Comment: ECML PKDD 201
Dynamic Tensor Decomposition via Neural Diffusion-Reaction Processes
Tensor decomposition is an important tool for multiway data analysis. In
practice, the data is often sparse yet associated with rich temporal
information. Existing methods, however, often under-use the time information
and ignore the structural knowledge within the sparsely observed tensor
entries. To overcome these limitations and to better capture the underlying
temporal structure, we propose Dynamic EMbedIngs fOr dynamic Tensor
dEcomposition (DEMOTE). We develop a neural diffusion-reaction process to
estimate dynamic embeddings for the entities in each tensor mode. Specifically,
based on the observed tensor entries, we build a multi-partite graph to encode
the correlation between the entities. We construct a graph diffusion process to
co-evolve the embedding trajectories of the correlated entities and use a
neural network to construct a reaction process for each individual entity. In
this way, our model can capture both the commonalities and personalities during
the evolution of the embeddings for different entities. We then use a neural
network to model the entry value as a nonlinear function of the embedding
trajectories. For model estimation, we combine ODE solvers to develop a
stochastic mini-batch learning algorithm. We propose a stratified sampling
method to balance the cost of processing each mini-batch so as to improve the
overall efficiency. We show the advantage of our approach in both simulation
study and real-world applications. The code is available at
https://github.com/wzhut/Dynamic-Tensor-Decomposition-via-Neural-Diffusion-Reaction-Processes
Multivariate Hawkes Processes for Large-scale Inference
In this paper, we present a framework for fitting multivariate Hawkes
processes for large-scale problems both in the number of events in the observed
history and the number of event types (i.e. dimensions). The proposed
Low-Rank Hawkes Process (LRHP) framework introduces a low-rank approximation of
the kernel matrix that allows to perform the nonparametric learning of the
triggering kernels using at most operations, where is the
rank of the approximation (). This comes as a major improvement to
the existing state-of-the-art inference algorithms that are in .
Furthermore, the low-rank approximation allows LRHP to learn representative
patterns of interaction between event types, which may be valuable for the
analysis of such complex processes in real world datasets. The efficiency and
scalability of our approach is illustrated with numerical experiments on
simulated as well as real datasets.Comment: 16 pages, 5 figure
Functional Regression
Functional data analysis (FDA) involves the analysis of data whose ideal
units of observation are functions defined on some continuous domain, and the
observed data consist of a sample of functions taken from some population,
sampled on a discrete grid. Ramsay and Silverman's 1997 textbook sparked the
development of this field, which has accelerated in the past 10 years to become
one of the fastest growing areas of statistics, fueled by the growing number of
applications yielding this type of data. One unique characteristic of FDA is
the need to combine information both across and within functions, which Ramsay
and Silverman called replication and regularization, respectively. This article
will focus on functional regression, the area of FDA that has received the most
attention in applications and methodological development. First will be an
introduction to basis functions, key building blocks for regularization in
functional regression methods, followed by an overview of functional regression
methods, split into three types: [1] functional predictor regression
(scalar-on-function), [2] functional response regression (function-on-scalar)
and [3] function-on-function regression. For each, the role of replication and
regularization will be discussed and the methodological development described
in a roughly chronological manner, at times deviating from the historical
timeline to group together similar methods. The primary focus is on modeling
and methodology, highlighting the modeling structures that have been developed
and the various regularization approaches employed. At the end is a brief
discussion describing potential areas of future development in this field
Distributed multi-agent Gaussian regression via finite-dimensional approximations
We consider the problem of distributedly estimating Gaussian processes in
multi-agent frameworks. Each agent collects few measurements and aims to
collaboratively reconstruct a common estimate based on all data. Agents are
assumed with limited computational and communication capabilities and to gather
noisy measurements in total on input locations independently drawn from a
known common probability density. The optimal solution would require agents to
exchange all the input locations and measurements and then invert an matrix, a non-scalable task. Differently, we propose two suboptimal
approaches using the first orthonormal eigenfunctions obtained from the
\ac{KL} expansion of the chosen kernel, where typically . The benefits
are that the computation and communication complexities scale with and not
with , and computing the required statistics can be performed via standard
average consensus algorithms. We obtain probabilistic non-asymptotic bounds
that determine a priori the desired level of estimation accuracy, and new
distributed strategies relying on Stein's unbiased risk estimate (SURE)
paradigms for tuning the regularization parameters and applicable to generic
basis functions (thus not necessarily kernel eigenfunctions) and that can again
be implemented via average consensus. The proposed estimators and bounds are
finally tested on both synthetic and real field data
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