Private Learning Implies Online Learning: An Efficient Reduction

We study the relationship between the notions of differentially private learning and online learning in games. Several recent works have shown that differentially private learning implies online learning, but an open problem of Neel, Roth, and Wu \cite{NeelAaronRoth2018} asks whether this implication is {\it efficient}. Specifically, does an efficient differentially private learner imply an efficient online learner? In this paper we resolve this open question in the context of pure differential privacy. We derive an efficient black-box reduction from differentially private learning to online learning from expert advice

Boosting Simple Learners

Boosting is a celebrated machine learning approach which is based on the idea of combining weak and moderately inaccurate hypotheses to a strong and accurate one. We study boosting under the assumption that the weak hypotheses belong to a class of bounded capacity. This assumption is inspired by the common convention that weak hypotheses are "rules-of-thumbs" from an "easy-to-learn class". (Schapire and Freund '12, Shalev-Shwartz and Ben-David '14.) Formally, we assume the class of weak hypotheses has a bounded VC dimension. We focus on two main questions: (i) Oracle Complexity: How many weak hypotheses are needed in order to produce an accurate hypothesis? We design a novel boosting algorithm and demonstrate that it circumvents a classical lower bound by Freund and Schapire ('95, '12). Whereas the lower bound shows that $\Omega({1}/{\gamma^2})$ weak hypotheses with $\gamma$-margin are sometimes necessary, our new method requires only $\tilde{O}({1}/{\gamma})$ weak hypothesis, provided that they belong to a class of bounded VC dimension. Unlike previous boosting algorithms which aggregate the weak hypotheses by majority votes, the new boosting algorithm uses more complex ("deeper") aggregation rules. We complement this result by showing that complex aggregation rules are in fact necessary to circumvent the aforementioned lower bound. (ii) Expressivity: Which tasks can be learned by boosting weak hypotheses from a bounded VC class? Can complex concepts that are "far away" from the class be learned? Towards answering the first question we identify a combinatorial-geometric parameter which captures the expressivity of base-classes in boosting. As a corollary we provide an affirmative answer to the second question for many well-studied classes, including half-spaces and decision stumps. Along the way, we establish and exploit connections with Discrepancy Theory.Comment: A minor revision according to STOC review

Online Admission Control and Embedding of Service Chains

The virtualization and softwarization of modern computer networks enables the definition and fast deployment of novel network services called service chains: sequences of virtualized network functions (e.g., firewalls, caches, traffic optimizers) through which traffic is routed between source and destination. This paper attends to the problem of admitting and embedding a maximum number of service chains, i.e., a maximum number of source-destination pairs which are routed via a sequence of to-be-allocated, capacitated network functions. We consider an Online variant of this maximum Service Chain Embedding Problem, short OSCEP, where requests arrive over time, in a worst-case manner. Our main contribution is a deterministic O(log L)-competitive online algorithm, under the assumption that capacities are at least logarithmic in L. We show that this is asymptotically optimal within the class of deterministic and randomized online algorithms. We also explore lower bounds for offline approximation algorithms, and prove that the offline problem is APX-hard for unit capacities and small L > 2, and even Poly-APX-hard in general, when there is no bound on L. These approximation lower bounds may be of independent interest, as they also extend to other problems such as Virtual Circuit Routing. Finally, we present an exact algorithm based on 0-1 programming, implying that the general offline SCEP is in NP and by the above hardness results it is NP-complete for constant L.Comment: early version of SIROCCO 2015 pape

O letramento e o ensino de literatura mediados por jogos digitais educacionais

A partir da dificuldade nacompreensão de textos literáriosque alunos do ensino médio apresentam, geralmente associada a pouca valoração da leitura, desenvolveu-se uma pesquisa que explora o jogo digital como motivador do interesse pela leitura de obras pertencentes ao sistema literário brasileiro, bem como no desenvolvimento do letramento deste aluno. A pesquisa apresenta resultados ainda preliminares e dá-se por meio de revisão bibliográfica, análises quanti/qualitativas, a formação de grupos de estudo com alunos de nível médio em instituições de ensino técnico e tecnológico e a criação de um fórum de discussão disponibilizado em uma importante rede social. O emprego do jogo a ser desenvolvido apoia-se nos conceitos de aprendizagem significativa, em estudos sobre a formação social da mente, bem como no conceito de zona de desenvolvimento proximal. Os sistemas de regras, a jogabilidade e a dimensão estética do jogo serão os diferenciais abordados como elementos motivacionais do aluno/leitor.XI Workshop tecnología informática aplicada en educaciónRed de Universidades con Carreras en Informática (RedUNCI

On the Complexity of Newman's Community Finding Approach for Biological and Social Networks

Given a graph of interactions, a module (also called a community or cluster) is a subset of nodes whose fitness is a function of the statistical significance of the pairwise interactions of nodes in the module. The topic of this paper is a model-based community finding approach, commonly referred to as modularity clustering, that was originally proposed by Newman and has subsequently been extremely popular in practice. Various heuristic methods are currently employed for finding the optimal solution. However, the exact computational complexity of this approach is still largely unknown. To this end, we initiate a systematic study of the computational complexity of modularity clustering. Due to the specific quadratic nature of the modularity function, it is necessary to study its value on sparse graphs and dense graphs separately. Our main results include a (1+\eps)-inapproximability for dense graphs and a logarithmic approximation for sparse graphs. We make use of several combinatorial properties of modularity to get these results. These are the first non-trivial approximability results beyond the previously known NP-hardness results.Comment: Journal of Computer and System Sciences, 201

On k-Column Sparse Packing Programs

We consider the class of packing integer programs (PIPs) that are column sparse, i.e. there is a specified upper bound k on the number of constraints that each variable appears in. We give an (ek+o(k))-approximation algorithm for k-column sparse PIPs, improving on recent results of $k^2\cdot 2^k$ and $O(k^2)$. We also show that the integrality gap of our linear programming relaxation is at least 2k-1; it is known that k-column sparse PIPs are $\Omega(k/ \log k)$-hard to approximate. We also extend our result (at the loss of a small constant factor) to the more general case of maximizing a submodular objective over k-column sparse packing constraints.Comment: 19 pages, v3: additional detail

The role of anion gap normalization time in the management of pediatric diabetic ketoacidosis

IntroductionOur aims were to determine whether anion gap normalization time (AGNT) correlates with risk factors related to the severity of diabetic ketoacidosis (DKA) in children, and to characterize AGNT as a criterion for DKA resolution in children admitted with moderate or severe disease.MethodsA ten-year retrospective cohort study of children admitted to the intensive care unit with DKA. We used a survival analysis approach to determine changes in serum glucose, bicarbonate, pH, and anion gap following admission. Using multivariate analysis, we examined associations between patients' demographic and laboratory characteristics with delayed normalization of the anion gap.ResultsA total of 95 patients were analyzed. The median AGNT was 8 h. Delayed AGNT (>8 h) correlated with pH < 7.1 and serum glucose >500 mg/dL. In multivariate analysis, glucose >500 mg/dL was associated with an increased risk for delayed AGNT, by 3.41 fold. Each 25 mg/dL elevation in glucose was associated with a 10% increment in risk for delayed AGNT. Median AGNT preceded median PICU discharge by 15 h (8 vs. 23 h).DiscussionAGNT represents a return to normal glucose-based physiology and an improvement in dehydration. The correlation observed between delayed AGNT and markers of DKA severity supports the usefulness of AGNT for assessing DKA recovery

On Approximating Four Covering and Packing Problems

In this paper, we consider approximability issues of the following four problems: triangle packing, full sibling reconstruction, maximum profit coverage and 2-coverage. All of them are generalized or specialized versions of set-cover and have applications in biology ranging from full-sibling reconstructions in wild populations to biomolecular clusterings; however, as this paper shows, their approximability properties differ considerably. Our inapproximability constant for the triangle packing problem improves upon the previous results; this is done by directly transforming the inapproximability gap of Haastad for the problem of maximizing the number of satisfied equations for a set of equations over GF(2) and is interesting in its own right. Our approximability results on the full siblings reconstruction problems answers questions originally posed by Berger-Wolf et al. and our results on the maximum profit coverage problem provides almost matching upper and lower bounds on the approximation ratio, answering a question posed by Hassin and Or.Comment: 25 page