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In this paper we review a wide spectrum of techniques which have been proposed in literature to enable acceptable recognition of language and text by machines. We discuss many techniques which have been proposed by researchers in the field of term weighting and explore the mathematical foundations of these methods. Term weighting schemes have broadly been classified as supervised and statistical methods and we present numerous examples from both categories to highlight the difference in approaches between the two broad categories. We pay particular attention to the Vector Space Model and its variants which form the basis of many of the other methods which have been discussed in the paper.

We introduce a new concept of solution to the KPZ equation which is shown to extend the classical Cole-Hopf solution. This notion provides a factorisation of the Cole-Hopf solution map into a \"universal\" measurable map from the probability space into an explicitly described auxiliary metric space, composed with a new solution map that has very good continuity properties. The advantage of such a formulation is that it essentially provides a pathwise notion of a solution, together with a very detailed approximation theory. In particular, our construction completely bypasses the Cole-Hopf transform, thus laying the groundwork for proving that the KPZ equation describes the fluctuations of systems in the KPZ universality class. As a corollary of our construction, we obtain very detailed new regularity results about the solution, as well as its derivative with respect to the initial condition. Other byproducts of the proof include an explicit approximation to the stationary solution of the KPZ equation, a well-posedness result for the Fokker-Planck equation associated to a particle diffusing in a rough space-time dependent potential, and a new periodic homogenisation result for the heat equation with a space-time periodic potential. One ingredient in our construction is an example of a non-Gaussian rough path such that the area process of its natural approximations needs to be renormalised by a diverging term for the approximations to converge.

Supervised machine learning studies are gaining more significant recently because of the availability of the increasing number of the electronic documents from different resources. Text classification can be defined that the task was automatically categorized a group documents into one or more predefined classes according to their subjects. Thereby, the major objective of text classification is to enable users for extracting information from textual resource and deals with process such as retrieval, classification, and machine learning techniques together in order to classify different pattern. In text classification technique, term weighting methods design suitable weights to the specific terms to enhance the text classification performance. This paper surveys of text classification, process of different term weighing methods and comparison between different classification techniques.

When estimating causal effects using observational data, it is desirable to replicate a randomized experiment as closely as possible by obtaining treated and control groups with similar covariate distributions. This goal can often be achieved by choosing well-matched samples of the original treated and control groups, thereby reducing bias due to the covariates. Since the 1970s, work on matching methods has examined how to best choose treated and control subjects for comparison. Matching methods are gaining popularity in fields such as economics, epidemiology, medicine and political science. However, until now the literature and related advice has been scattered across disciplines. Researchers who are interested in using matching methods—or developing methods related to matching—do not have a single place to turn to learn about past and current research. This paper provides a structure for thinking about matching methods and guidance on their use, coalescing the existing research (both old and new) and providing a summary of where the literature on matching methods is now and where it should be headed.

In 1979, Daniel Kahneman and Amos Tversky, published a paper in Econometrica titled “Prospect Theory: An Analysis of Decision under Risk.” The paper presented a new model of risk attitudes called “prospect theory,” which elegantly captured the experimental evidence on risk taking, including the documented violations of expected utility. More than 30 years later, prospect theory is still widely viewed as the best available description of how people evaluate risk in experimental settings. However, there are still relatively few well-known and broadly accepted applications of prospect theory in economics. One might be tempted to conclude that, even if prospect theory is an excellent description of behavior in experimental settings, it is less relevant outside the laboratory. In my view, this lesson would be incorrect. Over the past decade, researchers in the field of behavioral economics have put a lot of thought into how prospect theory should be applied in economic settings. This effort is bearing fruit. A significant body of theoretical work now incorporates the ideas in prospect theory into more traditional models of economic behavior, and a growing body of empirical work tests the predictions of these new theories. I am optimistic that some insights of prospect theory will eventually find a permanent and significant place in mainstream economic analysis.

This paper proposes entropy balancing, a data preprocessing method to achieve covariate balance in observational studies with binary treatments. Entropy balancing relies on a maximum entropy reweighting scheme that calibrates unit weights so that the reweighted treatment and control group satisfy a potentially large set of prespecified balance conditions that incorporate information about known sample moments. Entropy balancing thereby exactly adjusts inequalities in representation with respect to the first, second, and possibly higher moments of the covariate distributions. These balance improvements can reduce model dependence for the subsequent estimation of treatment effects. The method assures that balance improves on all covariate moments included in the reweighting. It also obviates the need for continual balance checking and iterative searching over propensity score models that may stochastically balance the covariate moments. We demonstrate the use of entropy balancing with Monte Carlo simulations and empirical applications.

The collection of Earth system models available in the archive of phase 5 of CMIP (CMIP5) represents, at least to some degree, a sample of uncertainty of future climate evolution. The presence of duplicated code as well as shared forcing and validation data in the multiple models in the archive raises at least three potential problems: biases in the mean and variance, the overestimation of sample size, and the potential for spurious correlations to emerge in the archive because of model replication. Analytical evidence is presented to demonstrate that the distribution of models in the CMIP5 archive is not consistent with a random sample, and a weighting scheme is proposed to reduce some aspects of model codependency in the ensemble. A method is proposed for selecting diverse and skillful subsets of models in the archive, which could be used for impact studies in cases where physically consistent joint projections of multiple variables (and their temporal and spatial characteristics) are required.

We formulate and carry out an analytical treatment of a single-period portfolio choice model featuring a reference point in wealth, S-shaped utility (value) functions with loss aversion, and probability weighting under Kahneman and Tversky's cumulative prospect theory (CPT). We introduce a new measure of loss aversion for large payoffs, called the large-loss aversion degree (LLAD), and show that it is a critical determinant of the well-posedness of the model. The sensitivity of the CPT value function with respect to the stock allocation is then investigated, which, as a by-product, demonstrates that this function is neither concave nor convex. We finally derive optimal solutions explicitly for the cases in which the reference point is the risk-free return and those in which it is not (while the utility function is piecewise linear), and we employ these results to investigate comparative statics of optimal risky exposures with respect to the reference point, the LLAD, and the curvature of the probability weighting. This paper was accepted by Wei Xiong, finance.

To capture the risk-aversion intuition, the standard approach in economics has been to utilize the model of expected utility, in which risk aversion derives from diminishing marginal utility for wealth (or diminishing marginal utility for aggregate consumption). The expected utility model for risk aversion has been used to derive many important insights. But over the years, economists and psychologists have identified various problematic issues with expected utility as a descriptive model of choice. In this article, we urge economists to take seriously the research agenda of developing and assessing different ways to model risk aversion. We proceed in three main steps. First, we highlight that the basic intuition of risk aversion that drives many results in economics is not intimately tied to expected utility. Second, we describe a few alternative models that can also capture the basic intuition of risk aversion. Finally, we discuss that, while expected utility and the alternative models might all capture the basic intuition of risk aversion, the alternative models can generate additional, more nuanced implications not shared with expected utility, that in some cases seem to be borne out by data. We emphasize that these alternative models also are not perfect, and further research is needed to identify even better approaches.