The maximum drawdown of the Brownian motion

The MDD is defined as the maximum loss incurred from peak to bottom during a specified period of time. It is often preferred over some of the other risk measures because of the tight relationship between large drawdowns and fund redemptions. Also, a large drawdown can even indicate the start of a deterioration of an otherwise successful trading system, for example due to a market regime switch. Overall, the MDD is a very important risk measure. To be able to use it more insightfully, its analytical properties have to be understood. As a step towards this direction, we have presented in this article some analytic results that we have developed. We hope more and more results will come out from the research community analyzing this important measure

A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II

Multi-objective evolutionary algorithms which use non-dominated sorting and sharing have been mainly criticized for their (i) O(MN3) computational complexity (where M is the number of objectives and N is the population size), (ii) non-elitism approach, and (iii) the need for specifying a sharing parameter. In this paper, we suggest a non-dominated sorting based multi-objective evolutionary algorithm (we called it the Non-dominated Sorting GA-II or NSGA-II) which alleviates all the above three difficulties. Specifically, a fast non-dominated sorting approach with O(MN2) computational complexity is presented. Second, a selection operator is presented which creates a mating pool by combining the parent and child populations and selecting the best (with respect to fitness and spread) N solutions. Simulation results on five difficult test problems show that the proposed NSGA-II, in most problems, is able to find much better spread of solutions and better convergence near the true Pareto-optimal front compared to PAES and SPEA-two other elitist multi-objective EAs which pay special attention towards creating a diverse Pareto-optimal front. Because of NSGA-II's low computational requirements, elitist approach, and parameter-less sharing approach, NSGA-II should find increasing applications in the years to come

Physiological responses of peanut (Arachis hypogaea L.) cultivars to water deficit stress: status of oxidative stress and antioxidant enzyme activities

From a field experiment, the changes in oxidative stress and antioxidant enzyme activities was studied in six Spanish peanut cultivars subjected to water deficit stress at two different stages viz. pegging and pod development stages. Imposition of water deficit stress significantly reduced relative water content, membrane stability and total carotenoid content in all the cultivars, whereas total chlorophyll content increased at initially and decreased at later stage. Chlorophyll a/b ratio increased under water deficit stress in most of the cultivars signifying greater damage to chlorophyll b rather than increase in chlorophyll a content. Oxidative stress measured in terms of H2O2 and superoxide radical content, and lipid peroxidation increased under water deficit stress, especially in susceptible cultivars viz. DRG 1, AK 159 and ICGV 86031. Relationship among different physiological parameters showed level of oxidative stress build-up was negatively correlated with activities of different antioxidant enzymes like superoxide dismutase, catalase, peroxidase, ascorbate peroxidase and glurathione reductase. The study concluded that in peanut water deficit stress at later stages of growth was more detrimental and an efficient antioxidant defense system manifested by higher activities of antioxidant enzymes was responsible for better stress tolerance in cultivars like ICGS 44 and TAG 24

RE-MOVE: An Adaptive Policy Design Approach for Dynamic Environments via Language-Based Feedback

Reinforcement learning-based policies for continuous control robotic navigation tasks often fail to adapt to changes in the environment during real-time deployment, which may result in catastrophic failures. To address this limitation, we propose a novel approach called RE-MOVE (\textbf{RE}quest help and \textbf{MOVE} on), which uses language-based feedback to adjust trained policies to real-time changes in the environment. In this work, we enable the trained policy to decide \emph{when to ask for feedback} and \emph{how to incorporate feedback into trained policies}. RE-MOVE incorporates epistemic uncertainty to determine the optimal time to request feedback from humans and uses language-based feedback for real-time adaptation. We perform extensive synthetic and real-world evaluations to demonstrate the benefits of our proposed approach in several test-time dynamic navigation scenarios. Our approach enable robots to learn from human feedback and adapt to previously unseen adversarial situations

Maximum Drawdown of a Brownian Motion and AlphaBoost: a Boosting Algorithm

We study two problems, one in the field of computational finance and the other one in machine learning. Firstly we study the Maximal drawdown statistics of the Brownian random walk. We give the infinite series representation of its distribution and consider its expected value. For the case when drift is zero, we give an exact expression of the expected value and for the other cases, we give an infinite series representation. For all the cases, we compute the limiting behavior of the expected value. Secondly, we propose a new algorithm for boosting, AlphaBoost, which does better than AdaBoost in reducing the cost function. We study its generalization properties and compare it to AdaBoost. However, this algorithm does not always give better out-of-sample performance.</p

Adaptive Learning Algorithms and Data Cloning

This thesis is in the field of machine learning: the use of data to automatically learn a hypothesis to predict the future behavior of a system. It summarizes three of my research projects. We first investigate the role of margins in the phenomenal success of the Boosting Algorithms. AdaBoost (Adaptive Boosting) is an algorithm for generating an ensemble of hypotheses for classification. The superior out-of-sample performance of AdaBoost has been attributed to the fact that it can generate a classifier which classifies the points with a large margin of confidence. This led to the development of many new algorithms focusing on optimizing the margin of confidence. It was observed that directly optimizing the margins leads to a poor performance. This apparent contradiction has been the topic of a long unresolved debate in the machine-learning community. We introduce new algorithms which are expressly designed to test the margin hypothesis and provide concrete evidence which refutes the margin argument. We then propose a novel algorithm for Adaptive sampling under Monotonicity constraint. The typical learning problem takes examples of the target function as input information and produces a hypothesis that approximates the target as an output. We consider a generalization of this paradigm by taking different types of information as input, and producing only specific properties of the target as output. This is a very common setup which occurs in many different real-life settings where the samples are expensive to obtain. We show experimentally that our algorithm achieves better performance than the existing methods, such as Staircase procedure and PEST. One of the major pitfalls in machine learning research is that of selection bias. This is mostly introduced unconsciously due to the choices made during the learning process, which often lead to over-optimistic estimates of the performance. In the third project, we introduce a new methodology for systematically reducing selection bias. Experiments show that using cloned datasets for model selection can lead to better performance and reduce the selection bias.</p

Mechanical component design for multiple objectives using elitist non-dominated sorting GA

Abstract. In this paper, we apply an elitist multi-objective genetic algorithm for solving mechanical component design problems with multiple objectives. Although there exists a number of classical techniques, evolutionary algorithms (EAs) have an edge over the classical methods in that they can find multiple Pareto-optimal solutions in one single simulation run. The proposed algorithm (we call NSGA-II) is a much improved version of the originally proposed nondominated sorting GA (NSGA) in that it is computationally faster, uses an elitist strategy, and it does not require fixing any niching parameter. On four mechanical component design problems borrowed from the literature, we show that the NSGA-II can find a much wider spread of solutions than classical methods and the NSGA. The results are encouraging and suggests immediate application of the proposed method to other more complex engineering design problems.

Numerical Study of the Behaviour of a Circular Footing on a Layered Granular Soil Under Vertical and Inclined Loading

This paper aims to study the behaviour of a circular footing resting on two granular layers, i.e., a dense sand layer resting on loose sand strata, subjected to a vertical and an inclined loading (α=0°, 10°, 20°, 30°) using the finite element (FE) software PLAXIS-3D. The Mohr-Coulomb criterion is employed for the analysis of the model, in which two parameters are considered to vary significantly; (1) thickness of the top layer (dense layer) and (2) friction angle (ф) of both the layers. In the circular footing, the bearing capacity on the layered soil profile is assessed using the mechanism of punching shear failure following the desired area approach. The punching shear failure mechanism formed in dense sand has a parabolic shape at the ultimate load when the maximum mobilization of shear force through the failure surface is taken into account, otherwise, the punching failure is the actual failure while punching in the lower layer continues to a greater extent, depending on the interface load. Bearing pressure decreases as the inclination increases with respect to the vertical, along with bearing pressure increasing as the thickness of the dense sand layer increases. The software results compare well with data available from the literature