17,996 research outputs found
Personalized Purchase Prediction of Market Baskets with Wasserstein-Based Sequence Matching
Personalization in marketing aims at improving the shopping experience of
customers by tailoring services to individuals. In order to achieve this,
businesses must be able to make personalized predictions regarding the next
purchase. That is, one must forecast the exact list of items that will comprise
the next purchase, i.e., the so-called market basket. Despite its relevance to
firm operations, this problem has received surprisingly little attention in
prior research, largely due to its inherent complexity. In fact,
state-of-the-art approaches are limited to intuitive decision rules for pattern
extraction. However, the simplicity of the pre-coded rules impedes performance,
since decision rules operate in an autoregressive fashion: the rules can only
make inferences from past purchases of a single customer without taking into
account the knowledge transfer that takes place between customers. In contrast,
our research overcomes the limitations of pre-set rules by contributing a novel
predictor of market baskets from sequential purchase histories: our predictions
are based on similarity matching in order to identify similar purchase habits
among the complete shopping histories of all customers. Our contributions are
as follows: (1) We propose similarity matching based on subsequential dynamic
time warping (SDTW) as a novel predictor of market baskets. Thereby, we can
effectively identify cross-customer patterns. (2) We leverage the Wasserstein
distance for measuring the similarity among embedded purchase histories. (3) We
develop a fast approximation algorithm for computing a lower bound of the
Wasserstein distance in our setting. An extensive series of computational
experiments demonstrates the effectiveness of our approach. The accuracy of
identifying the exact market baskets based on state-of-the-art decision rules
from the literature is outperformed by a factor of 4.0.Comment: Accepted for oral presentation at 25th ACM SIGKDD Conference on
Knowledge Discovery and Data Mining (KDD 2019
Algorithms on Ideal over Complex Multiplication order
We show in this paper that the Gentry-Szydlo algorithm for cyclotomic orders,
previously revisited by Lenstra-Silverberg, can be extended to
complex-multiplication (CM) orders, and even to a more general structure. This
algorithm allows to test equality over the polarized ideal class group, and
finds a generator of the polarized ideal in polynomial time. Also, the
algorithm allows to solve the norm equation over CM orders and the recent
reduction of principal ideals to the real suborder can also be performed in
polynomial time. Furthermore, we can also compute in polynomial time a unit of
an order of any number field given a (not very precise) approximation of it.
Our description of the Gentry-Szydlo algorithm is different from the original
and Lenstra- Silverberg's variant and we hope the simplifications made will
allow a deeper understanding. Finally, we show that the well-known speed-up for
enumeration and sieve algorithms for ideal lattices over power of two
cyclotomics can be generalized to any number field with many roots of unity.Comment: Full version of a paper submitted to ANT
Sparse approaches for the exact distribution of patterns in long state sequences generated by a Markov source
We present two novel approaches for the computation of the exact distribution
of a pattern in a long sequence. Both approaches take into account the sparse
structure of the problem and are two-part algorithms. The first approach relies
on a partial recursion after a fast computation of the second largest
eigenvalue of the transition matrix of a Markov chain embedding. The second
approach uses fast Taylor expansions of an exact bivariate rational
reconstruction of the distribution. We illustrate the interest of both
approaches on a simple toy-example and two biological applications: the
transcription factors of the Human Chromosome 5 and the PROSITE signatures of
functional motifs in proteins. On these example our methods demonstrate their
complementarity and their hability to extend the domain of feasibility for
exact computations in pattern problems to a new level
Euclidean distance geometry and applications
Euclidean distance geometry is the study of Euclidean geometry based on the
concept of distance. This is useful in several applications where the input
data consists of an incomplete set of distances, and the output is a set of
points in Euclidean space that realizes the given distances. We survey some of
the theory of Euclidean distance geometry and some of the most important
applications: molecular conformation, localization of sensor networks and
statics.Comment: 64 pages, 21 figure
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