1,254 research outputs found
STELAR: Spatio-temporal Tensor Factorization with Latent Epidemiological Regularization
Accurate prediction of the transmission of epidemic diseases such as COVID-19
is crucial for implementing effective mitigation measures. In this work, we
develop a tensor method to predict the evolution of epidemic trends for many
regions simultaneously. We construct a 3-way spatio-temporal tensor (location,
attribute, time) of case counts and propose a nonnegative tensor factorization
with latent epidemiological model regularization named STELAR. Unlike standard
tensor factorization methods which cannot predict slabs ahead, STELAR enables
long-term prediction by incorporating latent temporal regularization through a
system of discrete-time difference equations of a widely adopted
epidemiological model. We use latent instead of location/attribute-level
epidemiological dynamics to capture common epidemic profile sub-types and
improve collaborative learning and prediction. We conduct experiments using
both county- and state-level COVID-19 data and show that our model can identify
interesting latent patterns of the epidemic. Finally, we evaluate the
predictive ability of our method and show superior performance compared to the
baselines, achieving up to 21% lower root mean square error and 25% lower mean
absolute error for county-level prediction.Comment: AAAI 202
Fast Conical Hull Algorithms for Near-separable Non-negative Matrix Factorization
The separability assumption (Donoho & Stodden, 2003; Arora et al., 2012)
turns non-negative matrix factorization (NMF) into a tractable problem.
Recently, a new class of provably-correct NMF algorithms have emerged under
this assumption. In this paper, we reformulate the separable NMF problem as
that of finding the extreme rays of the conical hull of a finite set of
vectors. From this geometric perspective, we derive new separable NMF
algorithms that are highly scalable and empirically noise robust, and have
several other favorable properties in relation to existing methods. A parallel
implementation of our algorithm demonstrates high scalability on shared- and
distributed-memory machines.Comment: 15 pages, 6 figure
DYNAMIC POSITIVE EQUILIBRIUM PROBLEM
The Dynamic Positive Equilibrium Problem (DPEP) is a methodology for dealing with time series about economic agents decisions, regardless of the amount of available information. The approach is articulated in three phases, as in the static counterpart Symmetric Positive Equilibrium Problem (SPEP), with the variant that it must be preceded by the estimation of the equation of motion which characterizes a dynamic model. Furthermore, the definition of marginal cost in the DPEP model is different from the same notion in the static SPEP. In this paper, the DPEP approach was applied to a panel data dealing with annual crops from California agriculture for a horizon of eight years. The dynamic character of the DPEP model is based upon then assumption of output price adaptive expectations that follows a Nerlove-type specification.Research Methods/ Statistical Methods,
Retrospective Higher-Order Markov Processes for User Trails
Users form information trails as they browse the web, checkin with a
geolocation, rate items, or consume media. A common problem is to predict what
a user might do next for the purposes of guidance, recommendation, or
prefetching. First-order and higher-order Markov chains have been widely used
methods to study such sequences of data. First-order Markov chains are easy to
estimate, but lack accuracy when history matters. Higher-order Markov chains,
in contrast, have too many parameters and suffer from overfitting the training
data. Fitting these parameters with regularization and smoothing only offers
mild improvements. In this paper we propose the retrospective higher-order
Markov process (RHOMP) as a low-parameter model for such sequences. This model
is a special case of a higher-order Markov chain where the transitions depend
retrospectively on a single history state instead of an arbitrary combination
of history states. There are two immediate computational advantages: the number
of parameters is linear in the order of the Markov chain and the model can be
fit to large state spaces. Furthermore, by providing a specific structure to
the higher-order chain, RHOMPs improve the model accuracy by efficiently
utilizing history states without risks of overfitting the data. We demonstrate
how to estimate a RHOMP from data and we demonstrate the effectiveness of our
method on various real application datasets spanning geolocation data, review
sequences, and business locations. The RHOMP model uniformly outperforms
higher-order Markov chains, Kneser-Ney regularization, and tensor
factorizations in terms of prediction accuracy
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