Resilient Monotone Submodular Function Maximization

In this paper, we focus on applications in machine learning, optimization, and control that call for the resilient selection of a few elements, e.g. features, sensors, or leaders, against a number of adversarial denial-of-service attacks or failures. In general, such resilient optimization problems are hard, and cannot be solved exactly in polynomial time, even though they often involve objective functions that are monotone and submodular. Notwithstanding, in this paper we provide the first scalable, curvature-dependent algorithm for their approximate solution, that is valid for any number of attacks or failures, and which, for functions with low curvature, guarantees superior approximation performance. Notably, the curvature has been known to tighten approximations for several non-resilient maximization problems, yet its effect on resilient maximization had hitherto been unknown. We complement our theoretical analyses with supporting empirical evaluations.Comment: Improved suboptimality guarantees on proposed algorithm and corrected typo on Algorithm 1's statemen

A NEW UNBIASED ESTIMATOR OF A MULITPLE LINEAR REGRESSION MODEL OF THE CAPM IN CASE OF MULTICOLLINEARITY

In this work we propose an unbiased estimator for a multiple linear regression model of the CAPM in the presence of multicollinearity in the explanatory variables. Multicollinearity is a common problem in empirical Econometrics. The existing methods so far do not deal with cases of perfect multicollinearity. This new optimization method that belongs to the class of unbiased estimators is suitable for cases with strong or perfect multicollinearity, imposes restrictions of the minimizing matrix and produces small standard errors for the estimated parameters. At first we present the theoretical background of our approach and next we derive an expression for the covariance matrix of estimated coeffcients. As an example we estimate the basic linear regression model on Apple Inc expected stock returns and we examine multivariate extensions of this model in the special case of multicollinearity using the proposed method

Energy and Industrial Growth in India: The Next Emissions Superpower?

India is often referred to as the next development superpower and is widely seen as a potential destination for large scale manufacturing hubs. In this work we draw comparisons between India, Indonesia and China and find that all countries have a carbon intensive energy sector. However, there is a staggering difference between industrial energy intensity between them where India and Indonesia require double the amount of energy to produce the same output as China. We look into the decomposed industrial sectors and find that iron and steel and non-metallic minerals present the highest energy intensity in India. We argue that a production transition from China to India and Indonesia would result in a dangerous global emissions growth which has to be countered with rapid adoption of innovative energy technologies and policies

Statistical Learning for Analysis of Networked Control Systems over Unknown Channels

Recent control trends are increasingly relying on communication networks and wireless channels to close the loop for Internet-of-Things applications. Traditionally these approaches are model-based, i.e., assuming a network or channel model they are focused on stability analysis and appropriate controller designs. However the availability of such wireless channel modeling is fundamentally challenging in practice as channels are typically unknown a priori and only available through data samples. In this work we aim to develop algorithms that rely on channel sample data to determine the stability and performance of networked control tasks. In this regard our work is the first to characterize the amount of channel modeling that is required to answer such a question. Specifically we examine how many channel data samples are required in order to answer with high confidence whether a given networked control system is stable or not. This analysis is based on the notion of sample complexity from the learning literature and is facilitated by concentration inequalities. Moreover we establish a direct relation between the sample complexity and the networked system stability margin, i.e., the underlying packet success rate of the channel and the spectral radius of the dynamics of the control system. This illustrates that it becomes impractical to verify stability under a large range of plant and channel configurations. We validate our theoretical results in numerical simulations