360 research outputs found
Simple Asymmetric Exclusion Model and Lattice Paths: Bijections and Involutions
We study the combinatorics of the change of basis of three representations of
the stationary state algebra of the two parameter simple asymmetric exclusion
process. Each of the representations considered correspond to a different set
of weighted lattice paths which, when summed over, give the stationary state
probability distribution. We show that all three sets of paths are
combinatorially related via sequences of bijections and sign reversing
involutions.Comment: 28 page
SNE: Signed Network Embedding
Several network embedding models have been developed for unsigned networks.
However, these models based on skip-gram cannot be applied to signed networks
because they can only deal with one type of link. In this paper, we present our
signed network embedding model called SNE. Our SNE adopts the log-bilinear
model, uses node representations of all nodes along a given path, and further
incorporates two signed-type vectors to capture the positive or negative
relationship of each edge along the path. We conduct two experiments, node
classification and link prediction, on both directed and undirected signed
networks and compare with four baselines including a matrix factorization
method and three state-of-the-art unsigned network embedding models. The
experimental results demonstrate the effectiveness of our signed network
embedding.Comment: To appear in PAKDD 201
A combinatorial approach to jumping particles II: general boundary conditions
International audienceWe consider a model of particles jumping on a row, the TASEP. From the point of view of combinatorics a remarkable feauture of this Markov chain is that Catalan numbers are involved in several entries of its stationary distribution. In a companion paper, we gave a combinatorial interpretaion and a simple proof of these observations in the simplest case where the particles enter, jump and exit at the same rate. In this paper we show how to deal with general rates
Trends in bone metastasis modeling
Bone is one of the most common sites for cancer metastasis. Bone tissue is composed by different kinds of cells that coexist in a coordinated balance. Due to the complexity of bone, it is impossible to capture the intricate interactions between cells under either physiological or pathological conditions. Hence, a variety of in vivo and in vitro approaches have been developed. Various models of tumor\u2013bone diseases are routinely used to provide valuable information on the relationship between metastatic cancer cells and the bone tissue. Ideally, when modeling the metastasis of human cancers to bone, models would replicate the intra-tumor heterogeneity, as well as the genetic and phenotypic changes that occur with human cancers; such models would be scalable and reproducible to allow high-throughput investigation. Despite the continuous progress, there is still a lack of solid, amenable, and affordable models that are able to fully recapitulate the biological processes happening in vivo, permitting a correct interpretation of results. In the last decades, researchers have demonstrated that three-dimensional (3D) methods could be an innovative approach that lies between bi-dimensional (2D) models and animal models. Scientific evidence supports that the tumor microenvironment can be better reproduced in a 3D system than a 2D cell culture, and the 3D systems can be scaled up for drug screening in the same way as the 2D systems thanks to the current technologies developed. However, 3D models cannot completely recapitulate the inter-and intra-tumor heterogeneity found in patients. In contrast, ex vivo cultures of fragments of bone preserve key cell\u2013cell and cell\u2013matrix interactions and allow the study of bone cells in their natural 3D environment. Moreover, ex vivo bone organ cultures could be a better model to resemble the human pathogenic metastasis condition and useful tools to predict in vivo response to therapies. The aim of our review is to provide an overview of the current trends in bone metastasis modeling. By showing the existing in vitro and ex vivo systems, we aspire to contribute to broaden the knowledge on bone metastasis models and make these tools more appealing for further translational studies
Differentially Private Model Selection with Penalized and Constrained Likelihood
In statistical disclosure control, the goal of data analysis is twofold: The
released information must provide accurate and useful statistics about the
underlying population of interest, while minimizing the potential for an
individual record to be identified. In recent years, the notion of differential
privacy has received much attention in theoretical computer science, machine
learning, and statistics. It provides a rigorous and strong notion of
protection for individuals' sensitive information. A fundamental question is
how to incorporate differential privacy into traditional statistical inference
procedures. In this paper we study model selection in multivariate linear
regression under the constraint of differential privacy. We show that model
selection procedures based on penalized least squares or likelihood can be made
differentially private by a combination of regularization and randomization,
and propose two algorithms to do so. We show that our private procedures are
consistent under essentially the same conditions as the corresponding
non-private procedures. We also find that under differential privacy, the
procedure becomes more sensitive to the tuning parameters. We illustrate and
evaluate our method using simulation studies and two real data examples
Sharing Social Network Data: Differentially Private Estimation of Exponential-Family Random Graph Models
Motivated by a real-life problem of sharing social network data that contain
sensitive personal information, we propose a novel approach to release and
analyze synthetic graphs in order to protect privacy of individual
relationships captured by the social network while maintaining the validity of
statistical results. A case study using a version of the Enron e-mail corpus
dataset demonstrates the application and usefulness of the proposed techniques
in solving the challenging problem of maintaining privacy \emph{and} supporting
open access to network data to ensure reproducibility of existing studies and
discovering new scientific insights that can be obtained by analyzing such
data. We use a simple yet effective randomized response mechanism to generate
synthetic networks under -edge differential privacy, and then use
likelihood based inference for missing data and Markov chain Monte Carlo
techniques to fit exponential-family random graph models to the generated
synthetic networks.Comment: Updated, 39 page
BlinkML: Efficient Maximum Likelihood Estimation with Probabilistic Guarantees
The rising volume of datasets has made training machine learning (ML) models
a major computational cost in the enterprise. Given the iterative nature of
model and parameter tuning, many analysts use a small sample of their entire
data during their initial stage of analysis to make quick decisions (e.g., what
features or hyperparameters to use) and use the entire dataset only in later
stages (i.e., when they have converged to a specific model). This sampling,
however, is performed in an ad-hoc fashion. Most practitioners cannot precisely
capture the effect of sampling on the quality of their model, and eventually on
their decision-making process during the tuning phase. Moreover, without
systematic support for sampling operators, many optimizations and reuse
opportunities are lost.
In this paper, we introduce BlinkML, a system for fast, quality-guaranteed ML
training. BlinkML allows users to make error-computation tradeoffs: instead of
training a model on their full data (i.e., full model), BlinkML can quickly
train an approximate model with quality guarantees using a sample. The quality
guarantees ensure that, with high probability, the approximate model makes the
same predictions as the full model. BlinkML currently supports any ML model
that relies on maximum likelihood estimation (MLE), which includes Generalized
Linear Models (e.g., linear regression, logistic regression, max entropy
classifier, Poisson regression) as well as PPCA (Probabilistic Principal
Component Analysis). Our experiments show that BlinkML can speed up the
training of large-scale ML tasks by 6.26x-629x while guaranteeing the same
predictions, with 95% probability, as the full model.Comment: 22 pages, SIGMOD 201
Discretization of variational regularization in Banach spaces
Consider a nonlinear ill-posed operator equation where is
defined on a Banach space . In general, for solving this equation
numerically, a finite dimensional approximation of and an approximation of
are required. Moreover, in general the given data \yd of are noisy.
In this paper we analyze finite dimensional variational regularization, which
takes into account operator approximations and noisy data: We show
(semi-)convergence of the regularized solution of the finite dimensional
problems and establish convergence rates in terms of Bregman distances under
appropriate sourcewise representation of a solution of the equation. The more
involved case of regularization in nonseparable Banach spaces is discussed in
detail. In particular we consider the space of finite total variation
functions, the space of functions of finite bounded deformation, and the
--space
Deep Markov Random Field for Image Modeling
Markov Random Fields (MRFs), a formulation widely used in generative image
modeling, have long been plagued by the lack of expressive power. This issue is
primarily due to the fact that conventional MRFs formulations tend to use
simplistic factors to capture local patterns. In this paper, we move beyond
such limitations, and propose a novel MRF model that uses fully-connected
neurons to express the complex interactions among pixels. Through theoretical
analysis, we reveal an inherent connection between this model and recurrent
neural networks, and thereon derive an approximated feed-forward network that
couples multiple RNNs along opposite directions. This formulation combines the
expressive power of deep neural networks and the cyclic dependency structure of
MRF in a unified model, bringing the modeling capability to a new level. The
feed-forward approximation also allows it to be efficiently learned from data.
Experimental results on a variety of low-level vision tasks show notable
improvement over state-of-the-arts.Comment: Accepted at ECCV 201
Adversarial Personalized Ranking for Recommendation
Item recommendation is a personalized ranking task. To this end, many
recommender systems optimize models with pairwise ranking objectives, such as
the Bayesian Personalized Ranking (BPR). Using matrix Factorization (MF) ---
the most widely used model in recommendation --- as a demonstration, we show
that optimizing it with BPR leads to a recommender model that is not robust. In
particular, we find that the resultant model is highly vulnerable to
adversarial perturbations on its model parameters, which implies the possibly
large error in generalization.
To enhance the robustness of a recommender model and thus improve its
generalization performance, we propose a new optimization framework, namely
Adversarial Personalized Ranking (APR). In short, our APR enhances the pairwise
ranking method BPR by performing adversarial training. It can be interpreted as
playing a minimax game, where the minimization of the BPR objective function
meanwhile defends an adversary, which adds adversarial perturbations on model
parameters to maximize the BPR objective function. To illustrate how it works,
we implement APR on MF by adding adversarial perturbations on the embedding
vectors of users and items. Extensive experiments on three public real-world
datasets demonstrate the effectiveness of APR --- by optimizing MF with APR, it
outperforms BPR with a relative improvement of 11.2% on average and achieves
state-of-the-art performance for item recommendation. Our implementation is
available at: https://github.com/hexiangnan/adversarial_personalized_ranking.Comment: SIGIR 201
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