A test score based approach to stochastic submodular optimization

We study the canonical problem of maximizing a stochastic submodular function subject to a cardinality constraint, where the goal is to select a subset from a ground set of items with uncertain individual perfor- mances to maximize their expected group value. Although near-optimal algorithms have been proposed for this problem, practical concerns regarding scalability, compatibility with distributed implementation, and expensive oracle queries persist in large-scale applications. Motivated by online platforms that rely on indi- vidual item scores for content recommendation and team selection, we study a special class of algorithms that select items based solely on individual performance measures known as test scores. The central contribution of this work is a novel and systematic framework for designing test score based algorithms for a broad class of naturally occurring utility functions. We introduce a new scoring mechanism that we refer to as replication test scores and prove that as long as the objective function satisfies a diminishing returns condition, one can leverage these scores to compute solutions that are within a constant factor of the optimum. We then extend these scoring mechanisms to the more general stochastic submodular welfare maximization problem, where the goal is to partition items into groups to maximize the sum of the expected group values. For this more difficult problem, we show that replication test scores can be used to develop an algorithm that approximates the optimum solution up to a logarithmic factor. The techniques presented in this work bridge the gap between the rigorous theoretical work on submodular optimization and simple, scalable heuristics that are useful in certain domains. In particular, our results establish that in many applications involving the selection and assignment of items, one can design algorithms that are intuitive and practically relevant with only a small loss in performance compared to the state-of-the-art approaches

Test Score Algorithms for Budgeted Stochastic Utility Maximization

Motivated by recent developments in designing algorithms based on individual item scores for solving utility maximization problems, we study the framework of using test scores, defined as a statistic of observed individual item performance data, for solving the budgeted stochastic utility maximization problem. We extend an existing scoring mechanism, namely the replication test scores, to incorporate heterogeneous item costs as well as item values. We show that a natural greedy algorithm that selects items solely based on their replication test scores outputs solutions within a constant factor of the optimum for a broad class of utility functions. Our algorithms and approximation guarantees assume that test scores are noisy estimates of certain expected values with respect to marginal distributions of individual item values, thus making our algorithms practical and extending previous work that assumes noiseless estimates. Moreover, we show how our algorithm can be adapted to the setting where items arrive in a streaming fashion while maintaining the same approximation guarantee. We present numerical results, using synthetic data and data sets from the Academia.StackExchange Q&A forum, which show that our test score algorithm can achieve competitiveness, and in some cases better performance than a benchmark algorithm that requires access to a value oracle to evaluate function values

Pengaruh Atribut Produk Dan Word Of Mouth Terhadap Purchase Intention Transportasi Online Pada Konsumen Di Kota Surakarta

This study aims to determine (1) the effect of service quality on purchase intention, (2) the effect of product price on purchase intention, (3) the influence of word of mouth on purchase intention. The results of this study are expected to be taken into consideration of the company in berkompetitif on product prices, evaluate the quality of services, and form a word of mouth about whether the product attributes and word of mouth can affect consumer buying interest. This research is a quantitative research. The population in this study are consumers or users of online transport services in the city of Surakarta. Samples in this study were 100 respondents. Methods of data collection using convenience sampling withspreading google form and some distributing questionnaires personally. The analysis used in this research is test of research instrument, classical assumption test, multiple linear regression analysis test, F test, t test and coefficient of determination (R2). The result of research shows that R2 is 0,696 (69,6%) meaning that Purchase Intention variable can be explained by product attribute and word of mouth, the rest is 30,4% influenced by other variable not included in research model. Based on the result of the research, (1) the quality of service has no significant effect to purchase intention, (2) the price of the product has a positive effect on purchase intention, given by the company, the higher the buying interest of prospective consumers, (3) word of mouth positive effect on purchase intention, the more positive the word of mouth is, the higher consumer buying interest

Rotting infinitely many-armed bandits

We consider the infinitely many-armed bandit problem with rotting rewards, where the mean reward of an arm decreases at each pull of the arm according to an arbitrary trend with maximum rotting rate ϱ=o(1). We show that this learning problem has an Ω(max{ϱ1/3T,T−−√}) worst-case regret lower bound where T is the time horizon. We show that a matching upper bound O~(max{ϱ1/3T,T−−√}), up to a poly-logarithmic factor, can be achieved by an algorithm that uses a UCB index for each arm and a threshold value to decide whether to continue pulling an arm or remove the arm from further consideration, when the algorithm knows the value of the maximum rotting rate ϱ. We also show that an O~(max{ϱ1/3T,T3/4}) regret upper bound can be achieved by an algorithm that does not know the value of ϱ, by using an adaptive UCB index along with an adaptive threshold value

Field-Aligned Current During an Interval of BY-Dominated Interplanetary-Field; Modeled-to-Observed Comparisons

We model an interval of remarkable interplanetary magnetic field (IMF), for which we have a comprehensive set of observational data. This interval is associated with the arrival of an interplanetary coronal mass ejection. The solar wind densities at the time are particularly high and the IMF is primarily northward over many hours. This results in strong auroral emissions within the polar cap in a cusp spot, which we associate with lobe reconnection at the high-latitude magnetopause. We also observe areas of upwards field-aligned current (FAC) within the summer Northern Hemisphere polar cap that exhibit large current magnitudes. The model can reproduce the spatial distribution of the FACs well, even under changing conditions in the incoming IMF. Discrepancies exist between the modeled and observed current magnitudes. Notably, the winter Southern Hemisphere exhibits much lower current magnitudes overall. We also model a sharp transition of the location of magnetopause reconnection at the beginning of the interval, before the IMF remained northward for many hours. The reconnection location changed rapidly from a subsolar location at the low-latitude magnetopause under southward IMF conditions, to a high-latitude lobe reconnection location when the field is northward. This occurs during a fast rotation of the IMF at the shock front of a magnetic cloud

The orientation and current density of the magnetotail current sheet: A statistical study of the effect of geomagnetic conditions

We examine the orientation and current density of the current sheet during current sheet crossings from Cluster's 2001–2007 tail seasons. The curlometer technique is used to estimate the current density and is combined with Minimum Variance Analysis (MVA) to calculate the direction of the current sheet normal. The SYM-H and AE indices at the time of each crossing are employed to assess how the tilt angle (the angle the normal makes with the Z axis in the GSM YZ plane) and current density depend on geomagnetic conditions. Our results indicate a larger current sheet tilt in the YZ plane during intervals of stronger and/or more prolonged substorm activity, as indicated by the AE index. There is also evidence that when the ring current is enhanced during magnetic storms, the current sheet is less tilted even though the AE index is also disturbed. In addition larger current densities are seen during times of both magnetic storms and substorms, compared to crossings during only substorms and a quiet ring current. We conclude that increased substorm activity disrupts the current sheet structure resulting in greater motion of the current sheet (as found by Davey et al. (2012)) and a greater local tilt to the current sheet. We propose that the increased open flux in the tail during magnetic storms stabilizes the current sheet such that the tilt angle of the current sheet is reduced. The increased amount of open flux during magnetic storms also results in larger current densities within the current sheet

The Association of Cusp-Aligned Arcs With Plasma in the Magnetotail Implies a Closed Magnetosphere

We investigate a 15-day period in October 2011. Auroral observations by the Special Sensor Ultraviolet Spectrographic Imager instrument onboard the Defense Meteorological Satellite Program F16, F17, and F18 spacecraft indicate that the polar regions were covered by weak cusp-aligned arc (CAA) emissions whenever the interplanetary magnetic field (IMF) clock angle was small, |θ| < 45°, which amounted to 30% of the time. Simultaneous observations of ions and electrons in the tail by the Cluster C4 and Geotail spacecraft showed that during these intervals dense (≈1 cm−3) plasma was observed, even as far from the equatorial plane of the tail as |ZGSE| ≈ 13 RE. The ions had a pitch angle distribution peaking parallel and antiparallel to the magnetic field and the electrons had pitch angles that peaked perpendicular to the field. We interpret the counter-streaming ions and double loss-cone electrons as evidence that the plasma was trapped on closed field lines, and acted as a source for the CAA emission across the polar regions. This suggests that the magnetosphere was almost entirely closed during these periods. We further argue that the closure occurred as a consequence of dual-lobe reconnection. Our finding forces a significant re-evaluation of the magnetic topology of the magnetosphere during periods of northwards IMF

Modeling the magnetospheric X-ray emission from solar wind charge exchange with verification from XMM-Newton observations

An MHD‐based model of terrestrial solar wind charge exchange (SWCX) is created and compared to 19 case study observations in the 0.5–0.7 keV emission band taken from the European Photon Imaging Cameras on board XMM‐Newton. This model incorporates the Global Unified Magnetosphere‐Ionosphere Coupling Simulation‐4 MHD code and produces an X‐ray emission datacube from O7+ and O8+ emission lines around the Earth using in situ solar wind parameters as the model input. This study details the modeling process and shows that fixing the oxygen abundances to a constant value reduces the variance when comparing to the observations, at the cost of a small accuracy decrease in some cases. Using the ACE oxygen data returns a wide ranging accuracy, providing excellent correlation in a few cases and poor/anticorrelation in others. The sources of error for any user wishing to simulate terrestrial SWCX using an MHD model are described here and include mask position, hydrogen to oxygen ratio in the solar wind, and charge state abundances. A dawn‐dusk asymmetry is also found, similar to the results of empirical modeling. Using constant oxygen parameters, magnitudes approximately double that of the observed count rates are returned. A high accuracy is determined between the model and observations when comparing the count rate difference between enhanced SWCX and quiescent periods