Spectral Sparsification and Regret Minimization Beyond Matrix Multiplicative Updates

In this paper, we provide a novel construction of the linear-sized spectral sparsifiers of Batson, Spielman and Srivastava [BSS14]. While previous constructions required $\Omega(n^4)$ running time [BSS14, Zou12], our sparsification routine can be implemented in almost-quadratic running time $O(n^{2+\varepsilon})$. The fundamental conceptual novelty of our work is the leveraging of a strong connection between sparsification and a regret minimization problem over density matrices. This connection was known to provide an interpretation of the randomized sparsifiers of Spielman and Srivastava [SS11] via the application of matrix multiplicative weight updates (MWU) [CHS11, Vis14]. In this paper, we explain how matrix MWU naturally arises as an instance of the Follow-the-Regularized-Leader framework and generalize this approach to yield a larger class of updates. This new class allows us to accelerate the construction of linear-sized spectral sparsifiers, and give novel insights on the motivation behind Batson, Spielman and Srivastava [BSS14]

Online Local Learning via Semidefinite Programming

In many online learning problems we are interested in predicting local information about some universe of items. For example, we may want to know whether two items are in the same cluster rather than computing an assignment of items to clusters; we may want to know which of two teams will win a game rather than computing a ranking of teams. Although finding the optimal clustering or ranking is typically intractable, it may be possible to predict the relationships between items as well as if you could solve the global optimization problem exactly. Formally, we consider an online learning problem in which a learner repeatedly guesses a pair of labels (l(x), l(y)) and receives an adversarial payoff depending on those labels. The learner's goal is to receive a payoff nearly as good as the best fixed labeling of the items. We show that a simple algorithm based on semidefinite programming can obtain asymptotically optimal regret in the case where the number of possible labels is O(1), resolving an open problem posed by Hazan, Kale, and Shalev-Schwartz. Our main technical contribution is a novel use and analysis of the log determinant regularizer, exploiting the observation that log det(A + I) upper bounds the entropy of any distribution with covariance matrix A.Comment: 10 page

The Computational Power of Optimization in Online Learning

We consider the fundamental problem of prediction with expert advice where the experts are "optimizable": there is a black-box optimization oracle that can be used to compute, in constant time, the leading expert in retrospect at any point in time. In this setting, we give a novel online algorithm that attains vanishing regret with respect to $N$ experts in total $\widetilde{O}(\sqrt{N})$ computation time. We also give a lower bound showing that this running time cannot be improved (up to log factors) in the oracle model, thereby exhibiting a quadratic speedup as compared to the standard, oracle-free setting where the required time for vanishing regret is $\widetilde{\Theta}(N)$. These results demonstrate an exponential gap between the power of optimization in online learning and its power in statistical learning: in the latter, an optimization oracle---i.e., an efficient empirical risk minimizer---allows to learn a finite hypothesis class of size $N$ in time $O(\log{N})$. We also study the implications of our results to learning in repeated zero-sum games, in a setting where the players have access to oracles that compute, in constant time, their best-response to any mixed strategy of their opponent. We show that the runtime required for approximating the minimax value of the game in this setting is $\widetilde{\Theta}(\sqrt{N})$, yielding again a quadratic improvement upon the oracle-free setting, where $\widetilde{\Theta}(N)$ is known to be tight

Laboratory evaluation of diatomaceous earth against main stored product insects

The sensitivity of the main external and internal stored product insect pests to the commercial formulation of Detia Degesch Diatomaceous Earth – DDDE - Inerto (DE) was studied in laboratory experiments. The tested insects were adults of internal feeders Sitophilus oryzae Rhyzopertha dominica and external feeders Oryzaephilus surinamensis, Tribolium castaneum, and larvae (third instar) of T.castaneum. The DE was applied to wheat grain of 12% moisture content at concentrations of 0.5, 1.0, 2.0 and 4.0 g/kg of grain. The treated and untreated (control) grain were kept at 28°C and 65 ± 5% r.h. The numbers of dead and survived insects were counted two, three and four weeks after treatment. The number of adult progeny was counted nine weeks after treatment. At a concentration of 0.5 g/kg, mortality of S. oryzae and O. surinamensis after three weeks of exposure to DE were 92 and 86%, respectively. In contrast, mortality of T. castaneum and R. dominica adults was 3 and 37%, respectively. Progeny production of O. surinamensis and T. castaneum at a concentration of 2 g/kg was negligible, since only few individuals were recorded nine weeks after treatment, in comparison with the high progeny production in the control grain. The progeny of S. oryzae was also reduced. In contrast, for R. dominica was reduced only twice, in comparison with the control. In the case of T. castaneum larvae, at a concentration of 2 g/kg, after 4 weeks of exposure, 37% of the larvae emerged to adults, compared with 95% in control. Nine weeks after treatment, the number of F1adults was 100% suppressed. DE efficacy was similar at 4 g/kg. Based on the findings of the present study, the efficacy of the tested DE was influenced by DE concentration, insect species, developmental stage and exposure interval to the treated commodity.Keywords: Diatomaceous earth, Stored product insects, Wheat grai

Improvement of phosphine fumigation by the use of Speedbox

Today, phosphine is turning to be a major fumigant for controlling insects in stored products. However, few limitations, such as low temperatures and relatively long exposure time, limit the phosphine use. In order to improve phosphine application, a special devise, containing a heater and a ventilator, called "Speedbox" has been developed by Detia Degesch GmbH Germany. For studying the effectiveness of phosphine fumigation using Speedbox, we have conducted two kinds of experiments: one in a fumigation room (Pilot) and other in commercial warehouse. For pilot fumigation, adults, pupae and late larvae of Sitophilus oryzae, Rhyzopertha dominica, Oryzaephilus surinamensis, Trogoderma granarium and Callosobruchus maculatus, and all stages of Tribolium castaneum Herbst, Plodia interpunctella and Ephestia cautella were used as test insects. One to three Degesch Plates (about 2-6 g of phosphine gas per m3) were used. Exposure time was 1 to 3 days. The phosphine concentrtion was monitored by Bedfont device model 415. At 4 g/m3 for 48 ha maximum of phosphine concentration of 1460 ppm was reached. The total mortality of all tested insects and stages was recorded, except the eggs of E. cautella (98%). The commercial stack fumigation was done at the dosages of 2-4 g/m3, exposure time of 2-4 days and commodity temperatures of 6-17ºC. At a target concentration of 4 g/m3, 2 hours after beginning of the treatment, the concentration of the gas has reached 414 ppm, with a maximum of 1480 ppm. The total mortality of tested insects at adult, late larvae and pupae stages was recorded. The use of Speedbox allows one-day decrease in the plates degassing time, recirculation of the gas and its event distribution in the treated space and controlling major stored product insects for shorter exposure time at low temperatures. Keywords: Fumigation; Posphine; Speedbox; Stored-product insect

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

Direct Exoplanet Detection Using L1 Norm Low-Rank Approximation

We propose to use low-rank matrix approximation using the component-wise L1-norm for direct imaging of exoplanets. Exoplanet detection by direct imaging is a challenging task for three main reasons: (1) the host star is several orders of magnitude brighter than exoplanets, (2) the angular distance between exoplanets and star is usually very small, and (3) the images are affected by the noises called speckles that are very similar to the exoplanet signal both in shape and intensity. We first empirically examine the statistical noise assumptions of the L1 and L2 models, and then we evaluate the performance of the proposed L1 low-rank approximation (L1-LRA) algorithm based on visual comparisons and receiver operating characteristic (ROC) curves. We compare the results of the L1-LRA with the widely used truncated singular value decomposition (SVD) based on the L2 norm in two different annuli, one close to the star and one far away.Comment: 13 pages, 4 figures, BNAIC/BeNeLearn 202

Dynamics of Transformation from Segregation to Mixed Wealth Cities

We model the dynamics of the Schelling model for agents described simply by a continuously distributed variable - wealth. Agents move to neighborhoods where their wealth is not lesser than that of some proportion of their neighbors, the threshold level. As in the case of the classic Schelling model where segregation obtains between two races, we find here that wealth-based segregation occurs and persists. However, introducing uncertainty into the decision to move - that is, with some probability, if agents are allowed to move even though the threshold level condition is contravened - we find that even for small proportions of such disallowed moves, the dynamics no longer yield segregation but instead sharply transition into a persistent mixed wealth distribution. We investigate the nature of this sharp transformation between segregated and mixed states, and find that it is because of a non-linear relationship between allowed moves and disallowed moves. For small increases in disallowed moves, there is a rapid corresponding increase in allowed moves, but this tapers off as the fraction of disallowed moves increase further and finally settles at a stable value, remaining invariant to any further increase in disallowed moves. It is the overall effect of the dynamics in the initial region (with small numbers of disallowed moves) that shifts the system away from a state of segregation rapidly to a mixed wealth state. The contravention of the tolerance condition could be interpreted as public policy interventions like minimal levels of social housing or housing benefit transfers to poorer households. Our finding therefore suggests that it might require only very limited levels of such public intervention - just sufficient to enable a small fraction of disallowed moves, because the dynamics generated by such moves could spur the transformation from a segregated to mixed equilibrium.Comment: 12 pages, 7 figure