Bayesian Gene Set Analysis

Gene expression microarray technologies provide the simultaneous measurements of a large number of genes. Typical analyses of such data focus on the individual genes, but recent work has demonstrated that evaluating changes in expression across predefined sets of genes often increases statistical power and produces more robust results. We introduce a new methodology for identifying gene sets that are differentially expressed under varying experimental conditions. Our approach uses a hierarchical Bayesian framework where a hyperparameter measures the significance of each gene set. Using simulated data, we compare our proposed method to alternative approaches, such as Gene Set Enrichment Analysis (GSEA) and Gene Set Analysis (GSA). Our approach provides the best overall performance. We also discuss the application of our method to experimental data based on p53 mutation status

Testing significance of features by lassoed principal components

We consider the problem of testing the significance of features in high-dimensional settings. In particular, we test for differentially-expressed genes in a microarray experiment. We wish to identify genes that are associated with some type of outcome, such as survival time or cancer type. We propose a new procedure, called Lassoed Principal Components (LPC), that builds upon existing methods and can provide a sizable improvement. For instance, in the case of two-class data, a standard (albeit simple) approach might be to compute a two-sample $t$-statistic for each gene. The LPC method involves projecting these conventional gene scores onto the eigenvectors of the gene expression data covariance matrix and then applying an $L_1$ penalty in order to de-noise the resulting projections. We present a theoretical framework under which LPC is the logical choice for identifying significant genes, and we show that LPC can provide a marked reduction in false discovery rates over the conventional methods on both real and simulated data. Moreover, this flexible procedure can be applied to a variety of types of data and can be used to improve many existing methods for the identification of significant features.Comment: Published in at http://dx.doi.org/10.1214/08-AOAS182 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Inverse Ising inference using all the data

We show that a method based on logistic regression, using all the data, solves the inverse Ising problem far better than mean-field calculations relying only on sample pairwise correlation functions, while still computationally feasible for hundreds of nodes. The largest improvement in reconstruction occurs for strong interactions. Using two examples, a diluted Sherrington-Kirkpatrick model and a two-dimensional lattice, we also show that interaction topologies can be recovered from few samples with good accuracy and that the use of $l_1$-regularization is beneficial in this process, pushing inference abilities further into low-temperature regimes.Comment: 5 pages, 2 figures. Accepted versio

Analysis of Models for Decentralized and Collaborative AI on Blockchain

Machine learning has recently enabled large advances in artificial intelligence, but these results can be highly centralized. The large datasets required are generally proprietary; predictions are often sold on a per-query basis; and published models can quickly become out of date without effort to acquire more data and maintain them. Published proposals to provide models and data for free for certain tasks include Microsoft Research's Decentralized and Collaborative AI on Blockchain. The framework allows participants to collaboratively build a dataset and use smart contracts to share a continuously updated model on a public blockchain. The initial proposal gave an overview of the framework omitting many details of the models used and the incentive mechanisms in real world scenarios. In this work, we evaluate the use of several models and configurations in order to propose best practices when using the Self-Assessment incentive mechanism so that models can remain accurate and well-intended participants that submit correct data have the chance to profit. We have analyzed simulations for each of three models: Perceptron, Na\"ive Bayes, and a Nearest Centroid Classifier, with three different datasets: predicting a sport with user activity from Endomondo, sentiment analysis on movie reviews from IMDB, and determining if a news article is fake. We compare several factors for each dataset when models are hosted in smart contracts on a public blockchain: their accuracy over time, balances of a good and bad user, and transaction costs (or gas) for deploying, updating, collecting refunds, and collecting rewards. A free and open source implementation for the Ethereum blockchain and simulations written in Python is provided at https://github.com/microsoft/0xDeCA10B. This version has updated gas costs using newer optimizations written after the original publication.Comment: Accepted to ICBC 202

Foothill: A Quasiconvex Regularization for Edge Computing of Deep Neural Networks

Deep neural networks (DNNs) have demonstrated success for many supervised learning tasks, ranging from voice recognition, object detection, to image classification. However, their increasing complexity might yield poor generalization error that make them hard to be deployed on edge devices. Quantization is an effective approach to compress DNNs in order to meet these constraints. Using a quasiconvex base function in order to construct a binary quantizer helps training binary neural networks (BNNs) and adding noise to the input data or using a concrete regularization function helps to improve generalization error. Here we introduce foothill function, an infinitely differentiable quasiconvex function. This regularizer is flexible enough to deform towards $L_1$ and $L_2$ penalties. Foothill can be used as a binary quantizer, as a regularizer, or as a loss. In particular, we show this regularizer reduces the accuracy gap between BNNs and their full-precision counterpart for image classification on ImageNet.Comment: Accepted in 16th International Conference of Image Analysis and Recognition (ICIAR 2019

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

High-Dimensional Inference with the generalized Hopfield Model: Principal Component Analysis and Corrections

We consider the problem of inferring the interactions between a set of N binary variables from the knowledge of their frequencies and pairwise correlations. The inference framework is based on the Hopfield model, a special case of the Ising model where the interaction matrix is defined through a set of patterns in the variable space, and is of rank much smaller than N. We show that Maximum Lik elihood inference is deeply related to Principal Component Analysis when the amp litude of the pattern components, xi, is negligible compared to N^1/2. Using techniques from statistical mechanics, we calculate the corrections to the patterns to the first order in xi/N^1/2. We stress that it is important to generalize the Hopfield model and include both attractive and repulsive patterns, to correctly infer networks with sparse and strong interactions. We present a simple geometrical criterion to decide how many attractive and repulsive patterns should be considered as a function of the sampling noise. We moreover discuss how many sampled configurations are required for a good inference, as a function of the system size, N and of the amplitude, xi. The inference approach is illustrated on synthetic and biological data.Comment: Physical Review E: Statistical, Nonlinear, and Soft Matter Physics (2011) to appea

Evolving Spatially Aggregated Features from Satellite Imagery for Regional Modeling

Satellite imagery and remote sensing provide explanatory variables at relatively high resolutions for modeling geospatial phenomena, yet regional summaries are often desirable for analysis and actionable insight. In this paper, we propose a novel method of inducing spatial aggregations as a component of the machine learning process, yielding regional model features whose construction is driven by model prediction performance rather than prior assumptions. Our results demonstrate that Genetic Programming is particularly well suited to this type of feature construction because it can automatically synthesize appropriate aggregations, as well as better incorporate them into predictive models compared to other regression methods we tested. In our experiments we consider a specific problem instance and real-world dataset relevant to predicting snow properties in high-mountain Asia

Necessary and sufficient conditions of solution uniqueness in ℓ1\ell_1 minimization

This paper shows that the solutions to various convex $\ell_1$ minimization problems are \emph{unique} if and only if a common set of conditions are satisfied. This result applies broadly to the basis pursuit model, basis pursuit denoising model, Lasso model, as well as other $\ell_1$ models that either minimize $f(Ax-b)$ or impose the constraint $f(Ax-b)\leq\sigma$, where $f$ is a strictly convex function. For these models, this paper proves that, given a solution $x^*$ and defining I=\supp(x^*) and s=\sign(x^*_I), $x^*$ is the unique solution if and only if $A_I$ has full column rank and there exists $y$ such that $A_I^Ty=s$ and $|a_i^Ty|_\infty<1$ for $i\not\in I$. This condition is previously known to be sufficient for the basis pursuit model to have a unique solution supported on $I$. Indeed, it is also necessary, and applies to a variety of other $\ell_1$ models. The paper also discusses ways to recognize unique solutions and verify the uniqueness conditions numerically.Comment: 6 pages; revised version; submitte