Homin K. Lee

What Can We Learn Privately

Learning problems form an important category of computational tasks that generalizes many of the computations researchers apply to large real-life data sets. We ask: what concept classes can be learned privately, namely, by an algorithm whose output does not depend too heavily on any one input or specific training example? More precisely, we investigate learning algorithms that satisfy differential privacy, a notion that provides strong confidentiality guarantees in the contexts where aggregate information is released about a database containing sensitive information about individuals. We present several basic results that demonstrate general feasibility of private learning and relate several models previously studied separately in the contexts of privacy and standard learning.

Bioinformatic analysis of autism positional candidate genes using biological databases and computational gene network prediction

Common genetic disorders are believed to arise from the combined effects of multiple inherited genetic variants acting in concert with environmental factors, such that any given DNA sequence variant may have only a marginal effect on disease outcome. As a consequence, the correlation between disease status and any given DNA marker allele in a genomewide linkage study tends to be relatively weak and the implicated regions typically encompass hundreds of positional candidate genes. Therefore, new strategies are needed to parse relatively large sets of ‘positional’ candidate genes in search of actual disease‐related gene variants. Here we use biological databases to identify 383 positional candidate genes predicted by genomewide genetic linkage analysis of a large set of families, each with two or more members diagnosed with autism, or autism spectrum disorder (ASD). Next, we seek to identify a subset of biologically meaningful, high priority candidates. The strategy is to select autism candidate genes based on prior genetic evidence from the allelic association literature to query the known transcripts within the 1‐LOD (logarithm of the odds) support interval for each region. We use recently developed bioinformatic programs that automatically search the biological literature to predict pathways of interacting genes (pathwayassist and geneways). To identify gene regulatory networks, we search for coexpression between candidate genes and positional candidates. The studies are intended both to inform studies of autism, and to illustrate and explore the increasing potential of bioinformatic approaches as a compliment to linkage analysis.

Cryptographic strength of ssl/tls servers: current and recent practices

The Secure Socket Layer (SSL) and its variant, Transport Layer Security (TLS), are used toward ensuring server security. In this paper, we characterize the cryptographic strength of public servers running SSL/TLS. We present a tool developed for this purpose, the Probing SSL Security Tool (PSST), and evaluate over 19,000 servers. We expose the great diversity in the levels of cryptographic strength that is supported on the Internet. Some of our discouraging results show that most sites still support the insecure SSL 2.0, weak export-level grades of encryption ciphers, or weak RSA key strengths. We also observe encouraging behavior such as sensible default choices by servers when presented with multiple options, the quick adoption of AES (more than half the servers support strong key AES as their default choice), and the use of strong RSA key sizes of 1024 bits and above. Comparing results of running our tool over the last two years points to a positive trend that is moving in the right direction, though perhaps not as quickly as it should.

Learning random monotone DNF

We give an algorithm that with high probability properly learns random monotone DNF with t(n) terms of length ~logt(n) under the uniform distribution on the Boolean cube {0,1}^n. For any function t(n)@?poly(n) the algorithm runs in time poly(n,1/@e) and with high probability outputs an @e-accurate monotone DNF hypothesis. This is the first algorithm that can learn monotone DNF of arbitrary polynomial size in a reasonable average-case model of learning from random examples only. Our approach relies on the discovery and application of new Fourier properties of monotone functions which may be of independent interest.

DNF are teachable in the average case

We study the average number of well-chosen labeled examples that are required for a helpful teacher to uniquely specify a target function within a concept class. This “average teaching dimension” has been studied in learning theory and combinatorics and is an attractive alternative to the “worst-case” teaching dimension of Goldman and Kearns [7] which is exponential for many interesting concept classes. Recently Balbach [3] showed that the classes of 1-decision lists and 2-term DNF each have linear average teaching dimension. As our main result, we extend Balbach’s teaching result for 2-term DNF by showing that for any 1 ≤s ≤2

Learning Random Monotone DNF

^{\Theta({\it n})}

Optimal Cryptographic Hardness of Learning Monotone Functions

, the well-studied concept classes of at-most-s-term DNF and at-most-s-term monotone DNF each have average teaching dimension O(ns). The proofs use detailed analyses of the combinatorial structure of “most” DNF formulas and monotone DNF formulas. We also establish asymptotic separations between the worst-case and average teaching dimension for various other interesting Boolean concept classes such as juntas and sparse GF2 polynomials.

Separating Models of Learning from Correlated and Uncorrelated Data

We give an algorithm that with high probability properly learns random monotone DNF with t(n) terms of length ≈ logt(n) under the uniform distribution on the Boolean cube {0,1}n. For any function t(n) ≤ poly(n) the algorithm runs in time poly(n,1/i¾?) and with high probability outputs an i¾?-accurate monotone DNF hypothesis. This is the first algorithm that can learn monotone DNF of arbitrary polynomial size in a reasonable average-case model of learning from random examples only.

Coexpression Analysis of Human Genes Across Many Microarray Data Sets

A wide range of positive and negative results have been estab lished for learning different classes of Boolean functions from un iformly distributed random examples. However, polynomial-time algorithms hav e thus far been obtained almost exclusively for various classes of monotonefunctions, while the computational hardness results obtained to date have all be en for various classes of general (nonmonotone) functions. Motivated by this disp arity between known positive results (for monotone functions) and negative res ults (for nonmonotone functions), we establish strong computational limitation s on the efficient learnability of various classes of monotone functions. We give several such hardness results which are provably alm ost optimal since they nearly match known positive results. Some of our result s how cryptographic hardness of learning polynomial-size monotone circuits to accuracy only slightly greater than1/2 + 1/ √ n; this accuracy bound is close to optimal by known positive results (Blumet al., FOCS ’98). Other results show that under a plausible cryptographic hardness assumption, a class of constant-de pth, sub-polynomialsize circuits computing monotone functions is hard to learn ; this result is close to optimal in terms of the circuit size parameter by known posit ive results as well (Servedio, Information and Computation ’04). Our main tool is a complexitytheoretic approach to hardness amplification via noise sens itivity of monotone functions that was pioneered by O’Donnell (JCSS ’04).

ErmineJ: tool for functional analysis of gene expression data sets.

We consider a natural framework of learning from correlated data, in which successive examples used for learning are generated according to a random walk over the space of possible examples. Previous research has suggested that the Random Walk model is more powerful than comparable standard models of learning from independent examples, by exhibiting learning algorithms in the Random Walk framework that have no known counterparts in the standard model. We give strong evidence that the Random Walk model is indeed more powerful than the standard model, by showing that if any cryptographic one-way function exists (a universally held belief in public key cryptography), then there is a class of functions that can be learned efficiently in the Random Walk setting but not in the standard setting where all examples are independent.