131 research outputs found
Scalable Parallel Factorizations of SDD Matrices and Efficient Sampling for Gaussian Graphical Models
Motivated by a sampling problem basic to computational statistical inference,
we develop a nearly optimal algorithm for a fundamental problem in spectral
graph theory and numerical analysis. Given an SDDM matrix , and a constant , our algorithm gives efficient
access to a sparse linear operator such that
The
solution is based on factoring into a product of simple and
sparse matrices using squaring and spectral sparsification. For
with non-zero entries, our algorithm takes work nearly-linear in , and
polylogarithmic depth on a parallel machine with processors. This gives the
first sampling algorithm that only requires nearly linear work and i.i.d.
random univariate Gaussian samples to generate i.i.d. random samples for
-dimensional Gaussian random fields with SDDM precision matrices. For
sampling this natural subclass of Gaussian random fields, it is optimal in the
randomness and nearly optimal in the work and parallel complexity. In addition,
our sampling algorithm can be directly extended to Gaussian random fields with
SDD precision matrices
Model Selection for Topic Models via Spectral Decomposition
Abstract Topic models have achieved significant successes in analyzing large-scale text corpus. In practical applications, we are always confronted with the challenge of model selection, i.e., how to appropriately set the number of topics. Following the recent advances in topic models via tensor decomposition, we make a first attempt to provide theoretical analysis on model selection in latent Dirichlet allocation. With mild conditions, we derive the upper bound and lower bound on the number of topics given a text collection of finite size. Experimental results demonstrate that our bounds are correct and tight. Furthermore, using Gaussian mixture model as an example, we show that our methodology can be easily generalized to model selection analysis in other latent models
Towards Automated Neural Interaction Discovery for Click-Through Rate Prediction
Click-Through Rate (CTR) prediction is one of the most important machine
learning tasks in recommender systems, driving personalized experience for
billions of consumers. Neural architecture search (NAS), as an emerging field,
has demonstrated its capabilities in discovering powerful neural network
architectures, which motivates us to explore its potential for CTR predictions.
Due to 1) diverse unstructured feature interactions, 2) heterogeneous feature
space, and 3) high data volume and intrinsic data randomness, it is challenging
to construct, search, and compare different architectures effectively for
recommendation models. To address these challenges, we propose an automated
interaction architecture discovering framework for CTR prediction named
AutoCTR. Via modularizing simple yet representative interactions as virtual
building blocks and wiring them into a space of direct acyclic graphs, AutoCTR
performs evolutionary architecture exploration with learning-to-rank guidance
at the architecture level and achieves acceleration using low-fidelity model.
Empirical analysis demonstrates the effectiveness of AutoCTR on different
datasets comparing to human-crafted architectures. The discovered architecture
also enjoys generalizability and transferability among different datasets
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