Online Matrix Completion with Side Information

We give an online algorithm and prove novel mistake and regret bounds for online binary matrix completion with side information. The mistake bounds we prove are of the form $\tilde{O}(D/\gamma^2)$. The term $1/\gamma^2$ is analogous to the usual margin term in SVM (perceptron) bounds. More specifically, if we assume that there is some factorization of the underlying $m \times n$ matrix into $P Q^\intercal$ where the rows of $P$ are interpreted as "classifiers" in $\mathcal{R}^d$ and the rows of $Q$ as "instances" in $\mathcal{R}^d$, then $\gamma$ is the maximum (normalized) margin over all factorizations $P Q^\intercal$ consistent with the observed matrix. The quasi-dimension term $D$ measures the quality of side information. In the presence of vacuous side information, $D= m+n$. However, if the side information is predictive of the underlying factorization of the matrix, then in an ideal case, $D \in O(k + \ell)$ where $k$ is the number of distinct row factors and $\ell$ is the number of distinct column factors. We additionally provide a generalization of our algorithm to the inductive setting. In this setting, we provide an example where the side information is not directly specified in advance. For this example, the quasi-dimension $D$ is now bounded by $O(k^2 + \ell^2)$

Mapping the results of local statistics

The application of geographically weighted regression (GWR) – a local spatial statistical technique used to test for spatial nonstationarity – has grown rapidly in the social, health and demographic sciences. GWR is a useful exploratory analytical tool that generates a set of location-specific parameter estimates which can be mapped and analysed to provide information on spatial nonstationarity in relationships between predictors and the outcome variable. A major challenge to GWR users, however, is how best to map these parameter estimates. This paper introduces a simple mapping technique that combines local parameter estimates and local t-values on one map. The resultant map can facilitate the exploration and interpretation of nonstationarity.geographically weighted regression, local statistics, mapping, nonstationarity

A Design for a Security-typed Language with Certificate-based Declassification

This paper presents a calculus that supports information-flow security policies and certificate-based declassification. The decentralized label model and its downgrading mechanisms are concisely expressed in the polymorphic lambda calculus with subtyping (System F≾). We prove a conditioned version of the noninterference theorem such that authorization for declassification is justified by digital certificates from public-key infrastructures

Concise Concrete Syntax

We introduce a notion of ordered context-free grammars (OCFGs) with datatype tags to concisely specify grammars of programming languages. Our work is an extension of syntax definition formalism (SDF) and concrete datatypes that automate scanning, parsing, and syntax tree construction. But OCFGs also capture associativity and precedence at the level of production rules instead of lexical tokens such that a concrete syntax grammar is succinct enough be an abstract syntax definition. By expanding and re-indexing grammar symbols, OCFGs can be translated to grammars for standard lex and yacc such that existing and efficient parsing infrastructures can be reused. We have implemented a Java 5 compiler frontend with OCFGs. The complete grammar for such a realistic language fits comfortably in two pages of this paper, showing the practicality of our formalism

Run-time Principals in Information-flow Type Systems

Information-flow type systems are a promising approach for enforcing strong end-to-end confidentiality and integrity policies. Such policies, however, are usually specified in term of static information—data is labeled high or low security at compile time. In practice, the confidentiality of data may depend on information available only while the system is running. This paper studies language support for run-time principals, a mechanism for specifying information-flow security policies that depend on which principals interact with the system. We establish the basic property of noninterference for programs written in such language, and use run-time principals for specifying run-time authority in downgrading mechanisms such as declassification. In addition to allowing more expressive security policies, run-time principals enable the integration of language-based security mechanisms with other existing approaches such as Java stack inspection and public key infrastructures. We sketch an implementation of run-time principals via public keys such that principal delegation is verified by certificate chains

Run-time Principals in Information-flow Type Systems

Information-flow type systems are a promising approach for enforcing strong end-to-end confidentiality and integrity policies. Such policies, however, are usually specified in terms of static information — data is labeled high or low security at compile time. In practice, the confidentiality of data may depend on information available only while the system is running. This paper studies language support for run-time principals, a mechanism for specifying security policies that depend on which principals interact with the system. We establish the basic property of noninterference for programs written in such language, and use run-time principals for specifying run-time authority in downgrading mechanisms such as declassification. In addition to allowing more expressive security policies, run-time principals enable the integration of language-based security mechanisms with other existing approaches such as Java stack inspection and public key infrastructures. We sketch an implementation of run-time principals via public keys such that principal delegation is verified by certificate chains

Online Multitask Learning with Long-Term Memory

We introduce a novel online multitask setting. In this setting each task is partitioned into a sequence of segments that is unknown to the learner. Associated with each segment is a hypothesis from some hypothesis class. We give algorithms that are designed to exploit the scenario where there are many such segments but significantly fewer associated hypotheses. We prove regret bounds that hold for any segmentation of the tasks and any association of hypotheses to the segments. In the single-task setting this is equivalent to switching with long-term memory in the sense of [Bousquet and Warmuth; 2003]. We provide an algorithm that predicts on each trial in time linear in the number of hypotheses when the hypothesis class is finite. We also consider infinite hypothesis classes from reproducing kernel Hilbert spaces for which we give an algorithm whose per trial time complexity is cubic in the number of cumulative trials. In the single-task special case this is the first example of an efficient regret-bounded switching algorithm with long-term memory for a non-parametric hypothesis class

Unemployment and Opioid-Related Mortality Rates in U.S. Counties: Investigating Social Capital and Social Isolation–Smoking Pathways

We examine two mechanisms—social capital and sociobehavior—potentially linking unemployment rates to opioid-related mortality and investigate whether the mechanisms differ geographically by the pace of the opioid crisis. Applying path analysis techniques to 2015–2017 opioid-related mortality in U.S. counties (N = 2,648), we find that (1) high unemployment rates are not directly associated with opioid-related mortality rates; (2) high unemployment rates are negatively associated with social capital, and low social capital contributes to high opioid-related mortality; (3) high unemployment rates increase social isolation and the prevalence of smoking, which is positively related to opioid-related mortality; and (4) the pathways are stronger among counties in the states experiencing a rapid growth in opioid-related mortality rates than among those states that are not. Our findings offer insight into how unemployment rates shape the opioid crisis and suggest that the relationship between unemployment and opioid-related mortality is complex