Akshay Krishnamurthy

DEGAS: De Novo Discovery of Dysregulated Pathways in Human Diseases

Background Molecular studies of the human disease transcriptome typically involve a search for genes whose expression is significantly dysregulated in sick individuals compared to healthy controls. Recent studies have found that only a small number of the genes in human disease-related pathways show consistent dysregulation in sick individuals. However, those studies found that some pathway genes are affected in most sick individuals, but genes can differ among individuals. While a pathway is usually defined as a set of genes known to share a specific function, pathway boundaries are frequently difficult to assign, and methods that rely on such definition cannot discover novel pathways. Protein interaction networks can potentially be used to overcome these problems. Methodology/Principal Findings We present DEGAS (DysrEgulated Gene set Analysis via Subnetworks), a method for identifying connected gene subnetworks significantly enriched for genes that are dysregulated in specimens of a disease. We applied DEGAS to seven human diseases and obtained statistically significant results that appear to home in on compact pathways enriched with hallmarks of the diseases. In Parkinsons disease, we provide novel evidence for involvement of mRNA splicing, cell proliferation, and the 14-3-3 complex in the disease progression. DEGAS is available as part of the MATISSE software package (http://acgt.cs.tau.ac.il/matisse). Conclusions/Significance The subnetworks identified by DEGAS can provide a signature of the disease potentially useful for diagnosis, pinpoint possible pathways affected by the disease, and suggest targets for drug intervention.

Fine-grained privilege separation for web applications

We present a programming model for building web applications with security properties that can be confidently verified during a security review. In our model, applications are divided into isolated, privilege-separated components, enabling rich security policies to be enforced in a way that can be checked by reviewers. In our model, the web framework enforces privilege separation and isolation of web applications by requiring the use of an object-capability language and providing interfaces that expose limited, explicitly-specified privileges to application components. This approach restricts what each component of the application can do and quarantines buggy or compromised code. It also provides a way to more safely integrate third-party, less-trusted code into a web application. We have implemented a prototype of this model based upon the Java Servlet framework and used it to build a webmail application. Our experience with this example suggests that the approach is viable and helpful at establishing reviewable application-specific security properties.

Robust multi-source network tomography using selective probes

Knowledge of a networks topology and internal characteristics such as delay times or losses is crucial to maintain seamless operation of network services. Network tomography is a useful approach to infer such knowledge from end-to-end measurements between nodes at the periphery of the network, as it does not require cooperation of routers and other internal nodes. Most current tomography algorithms are single-source methods, which use multicast probes or synchronized unicast packet trains to measure covariances between destinations from a single vantage point and recover a tree topology from these measurements. Multi-source tomography, on the other hand, uses pairwise hop counts or latencies and consequently overcomes the difficulties associated with obtaining measurements for single-source methods. However, topology recovery is complicated by the fact that the paths along which measurements are taken do not form a tree in the network. Motivated by recent work suggesting that these measurements can be well-approximated by tree metrics, we present two algorithms that use selective pairwise distance measurements between peripheral nodes to construct a tree whose end-to-end distances approximate those in the network. Our first algorithm accommodates measurements perturbed by additive noise, while our second considers a novel noise model that captures missing measurements and the networks deviations from a tree topology. Both algorithms provably use O (p polylog p) pairwise measurements to construct a tree approximation on p end hosts. We present extensive simulated and real-world experiments to evaluate both of our algorithms.

Subspace learning from extremely compressed measurements

We consider learning the principal subspace of a large set of vectors from an extremely small number of compressive measurements of each vector. Our theoretical results show that even a constant number of measurements per column suffices to approximate the principal subspace to arbitrary precision, provided that the number of vectors is large. This result is achieved by a simple algorithm that computes the eigenvectors of an estimate of the covariance matrix. The main insight is to exploit an averaging effect that arises from applying a different random projection to each vector. We provide a number of simulations confirming our theoretical results.

Completion of high-rank ultrametric matrices using selective entries

Ultrametric matrices are hierarchically structured matrices that arise naturally in many scenarios, e.g. delay covariance of packets sent from a source to a set of clients in a computer network, interactions between multi-scale communities in a social network, and genome sequence alignment scores in phylogenetic tree reconstruction problems. In this work, we show that it is possible to complete n × n ultrametric matrices using only n log n entries. Since ultrametric matrices are high-rank matrices, our results extend recent work on completion of n×n low-rank matrices that requires n log n randomly sampled entries. In the ultrametric setting, a random sampling of entries does not suffice, and we require selective sampling of entries using feedback obtained from entries observed at a previous stage.

A Hierarchical Algorithm for Extreme Clustering

Many modern clustering methods scale well to a large number of data points, N, but not to a large number of clusters, K. This paper introduces PERCH, a new non-greedy, incremental algorithm for hierarchical clustering that scales to both massive N and K---a problem setting we term extreme clustering. Our algorithm efficiently routes new data points to the leaves of an incrementally-built tree. Motivated by the desire for both accuracy and speed, our approach performs tree rotations for the sake of enhancing subtree purity and encouraging balancedness. We prove that, under a natural separability assumption, our non-greedy algorithm will produce trees with perfect dendrogram purity regardless of data arrival order. Our experiments demonstrate that PERCH constructs more accurate trees than other tree-building clustering algorithms and scales well with both N and K, achieving a higher quality clustering than the strongest flat clustering competitor in nearly half the time.

Minimax structured normal means inference

We provide a unified treatment of a broad class of noisy structure recovery problems, known as structured normal means inference. In this setting, the goal is to identify, from a finite collection of Gaussian distributions with different means, the distribution that produced some observed data. Recent work has studied several special cases including sparse vectors, biclusters, and graph-based structures. We establish nearly matching upper and lower bounds on the minimax probability of error for any structured normal means problem, and we derive an optimality certificate for the maximum likelihood estimator, which can be applied to many instantiations. We also consider an experimental design setting, where we generalize our minimax bounds and derive an algorithm for computing a design strategy with a certain optimality property. We show that our results give tight minimax bounds for many structure recovery problems and consider some consequences for interactive sampling.