Label optimal regret bounds for online local learning

We resolve an open question from (Christiano, 2014b) posed in COLT'14 regarding the optimal dependency of the regret achievable for online local learning on the size of the label set. In this framework the algorithm is shown a pair of items at each step, chosen from a set of $n$ items. The learner then predicts a label for each item, from a label set of size $L$ and receives a real valued payoff. This is a natural framework which captures many interesting scenarios such as collaborative filtering, online gambling, and online max cut among others. (Christiano, 2014a) designed an efficient online learning algorithm for this problem achieving a regret of $O(\sqrt{nL^3T})$, where $T$ is the number of rounds. Information theoretically, one can achieve a regret of $O(\sqrt{n \log L T})$. One of the main open questions left in this framework concerns closing the above gap. In this work, we provide a complete answer to the question above via two main results. We show, via a tighter analysis, that the semi-definite programming based algorithm of (Christiano, 2014a), in fact achieves a regret of $O(\sqrt{nLT})$. Second, we show a matching computational lower bound. Namely, we show that a polynomial time algorithm for online local learning with lower regret would imply a polynomial time algorithm for the planted clique problem which is widely believed to be hard. We prove a similar hardness result under a related conjecture concerning planted dense subgraphs that we put forth. Unlike planted clique, the planted dense subgraph problem does not have any known quasi-polynomial time algorithms. Computational lower bounds for online learning are relatively rare, and we hope that the ideas developed in this work will lead to lower bounds for other online learning scenarios as well.Comment: 13 pages; Changes from previous version: small changes to proofs of Theorems 1 & 2, a small rewrite of introduction as well (this version is the same as camera-ready copy in COLT '15

Evaluating Asset Pricing Implications of DSGE Models

This paper conducts an econometric evaluation of structural macroeconomic asset pricing models. A one-sector dynamic stochastic general equilibrium model (DSGE) with habit formation and capital adjustment costs is considered. Based on the log-linearized DSGE model, a Gaussian probability model for the joint distribution of aggregate consumption, investment, and a vector of asset returns R(t) is specified. We facilitate the stochastic discount factor M(t) representation obtained from the DSGE model and impose the no-arbitrage condition E[M(t)R(t)|t-1]=1. In addition to the full general equilibrium model, we also consider consumption and production based partial equilibrium specifications, and a more general reference model. To evaluate the various asset pricing models we compute posterior model probabilities and loss function based measures of model adequacy.

Navigating Central Path with Electrical Flows: from Flows to Matchings, and Back

We present an $\tilde{O}(m^{10/7})=\tilde{O}(m^{1.43})$-time algorithm for the maximum s-t flow and the minimum s-t cut problems in directed graphs with unit capacities. This is the first improvement over the sparse-graph case of the long-standing $O(m \min(\sqrt{m},n^{2/3}))$ time bound due to Even and Tarjan [EvenT75]. By well-known reductions, this also establishes an $\tilde{O}(m^{10/7})$-time algorithm for the maximum-cardinality bipartite matching problem. That, in turn, gives an improvement over the celebrated celebrated $O(m \sqrt{n})$ time bound of Hopcroft and Karp [HK73] whenever the input graph is sufficiently sparse

Electrical Flows, Laplacian Systems, and Faster Approximation of Maximum Flow in Undirected Graphs

We introduce a new approach to computing an approximately maximum s-t flow in a capacitated, undirected graph. This flow is computed by solving a sequence of electrical flow problems. Each electrical flow is given by the solution of a system of linear equations in a Laplacian matrix, and thus may be approximately computed in nearly-linear time. Using this approach, we develop the fastest known algorithm for computing approximately maximum s-t flows. For a graph having n vertices and m edges, our algorithm computes a (1-\epsilon)-approximately maximum s-t flow in time \tilde{O}(mn^{1/3} \epsilon^{-11/3}). A dual version of our approach computes a (1+\epsilon)-approximately minimum s-t cut in time \tilde{O}(m+n^{4/3}\eps^{-8/3}), which is the fastest known algorithm for this problem as well. Previously, the best dependence on m and n was achieved by the algorithm of Goldberg and Rao (J. ACM 1998), which can be used to compute approximately maximum s-t flows in time \tilde{O}(m\sqrt{n}\epsilon^{-1}), and approximately minimum s-t cuts in time \tilde{O}(m+n^{3/2}\epsilon^{-3})

Elevated expression of type VII collagen in the skin of patients with systemic sclerosis. Regulation by transforming growth factor-beta.

A hallmark of systemic sclerosis (SSc) is the development of tissue fibrosis. Excessive production of several connective tissue components normally present in the dermis, including type I, III, V, and VI collagens as well as fibronectin and proteoglycans, is a consistent finding in the skin of SSc patients. Type VII collagen is a major constituent of anchoring fibrils, present in the skin at the dermal-epidermal basement membrane zone. TGF-beta has been shown to upregulate the expression of the type VII collagen gene. In this study, we assessed the expression of type VII collagen and TGF-beta in the skin of patients with SSc. Indirect immunofluorescence showed an abundance of type VII collagen in the patients\u27 skin, including the dermis. Ultrastructural analysis of SSc skin revealed an abundance of fibrillar material, possibly representing type VII collagen. The increased expression of type VII collagen epitopes was accompanied by the elevated expression of immunodetectable TGF-beta 1 and TGF-beta 2. Dermal fibroblasts cultured from the affected individuals showed a statistically significant (P \u3c 0.02) increase in the expression of type VII collagen at the mRNA level, as detected by reverse transcription-PCR with a mutated cDNA as an internal standard, and increased deposition of the protein as assessed by indirect immunofluorescence. Thus, type VII collagen is abundantly present in SSc patients\u27 dermis, a location not characteristic of its normal distribution, and its aberrant expression may relate to the presence of TGF-beta in the same topographic distribution. The presence of type VII collagen in the dermis may contribute to the tightly bound and indurated appearance of the affected skin in SSc patients

Alopecia areata: a multifactorial autoimmune condition

Alopecia areata is an autoimmune disease that results in non-scarring hair loss, and it is clinically characterised by small patches of baldness on the scalp and/or around the body. It can later progress to total loss of scalp hair (Alopecia totalis) and/or total loss of all body hair (Alopecia universalis). The rapid rate of hair loss and disfiguration caused by the condition causes anxiety on patients and increases the risks of developing psychological and psychiatric complications. Hair loss in alopecia areata is caused by lymphocytic infiltrations around the hair follicles and IFN-γ. IgG antibodies against the hair follicle cells are also found in alopecia areata sufferers. In addition, the disease coexists with other autoimmune disorders and can come secondary to infections or inflammation. However, despite the growing knowledge about alopecia areata, the aetiology and pathophysiology of disease are not well defined. In this review we discuss various genetic and environmental factors that cause autoimmunity and describe the immune mechanisms that lead to hair loss in alopecia areata patients

Faster Approximate Multicommodity Flow Using Quadratically Coupled Flows

The maximum multicommodity flow problem is a natural generalization of the maximum flow problem to route multiple distinct flows. Obtaining a $1-\epsilon$ approximation to the multicommodity flow problem on graphs is a well-studied problem. In this paper we present an adaptation of recent advances in single-commodity flow algorithms to this problem. As the underlying linear systems in the electrical problems of multicommodity flow problems are no longer Laplacians, our approach is tailored to generate specialized systems which can be preconditioned and solved efficiently using Laplacians. Given an undirected graph with m edges and k commodities, we give algorithms that find $1-\epsilon$ approximate solutions to the maximum concurrent flow problem and the maximum weighted multicommodity flow problem in time \tilde{O}(m^{4/3}\poly(k,\epsilon^{-1}))