In this article, we will look at the difference between generative and discriminative models, how they contrast, and one another. Discriminative machine learning is to recognize the rig output among possible output choices. Given something about the data, and done by learning parameters. Classification is additionally mentioned as discriminative modeling. This is often on the grounds; the model must separate instances of input variables across classes.

That's the question faced by Prakash Shenoy, the Ronald G. Harper Distinguished Professor of Artificial Intelligence at the University of Kansas School of Business. His answer can be found in the article "An Interval-Valued Utility Theory for Decision Making with Dempster-Shafer Belief Functions," which appears in the September issue of the International Journal of Approximate Reasoning. "People assume that you can always attach probabilities to uncertain events," Shenoy said. "But in real life, you never know what the probabilities are. You don't know if it's 50 percent or 60 percent. This is the essence of the theory of belief functions that Arthur Dempster and Glenn Shafer formulated in the 1970s."

Risk specialists are trying to understand risk better and use complex models for risk assessment, while many risks are not yet well understood. The lack of empirical data and complex causal and outcome relationships make it difficult to estimate the degree to which certain risk types are exposed. Traditional risk models are based on classical set theory. In comparison, fuzzy logic models are built on fuzzy set theory and are useful for analyzing risks with insufficient knowledge or inaccurate data. Fuzzy logic systems help to make large-scale risk management frameworks more simple. For risks that do not have an appropriate probability model, a fuzzy logic system can help model the cause and effect relationships, assess the level of risk exposure, rank key risks in a consistent way, and consider available data and experts'opinions. Besides, in fuzzy logic systems, some rules explicitly explain the connection, dependence, and relationships between model factors. This can help identify risk mitigation solutions. Resources can be used to mitigate risks with very high levels of exposure and relatively low hedging costs. Fuzzy set and fuzzy logic models can be used with Bayesian and other types of method recognition and decision models, including artificial neural networks and decision tree models. These developed models have the potential to solve difficult risk assessment problems. This research paper explores areas in which fuzzy logic models can be used to improve risk assessment and risk decision making. We will discuss the methodology, framework, and process of using fuzzy logic systems in risk assessment.

This paper considers the problem of estimating the information leakage of a system in the black-box scenario. It is assumed that the system's internals are unknown to the learner, or anyway too complicated to analyze, and the only available information are pairs of input-output data samples, possibly obtained by submitting queries to the system or provided by a third party. Previous research has mainly focused on counting the frequencies to estimate the input-output conditional probabilities (referred to as frequentist approach), however this method is not accurate when the domain of possible outputs is large. To overcome this difficulty, the estimation of the Bayes error of the ideal classifier was recently investigated using Machine Learning (ML) models and it has been shown to be more accurate thanks to the ability of those models to learn the input-output correspondence. However, the Bayes vulnerability is only suitable to describe one-try attacks. A more general and flexible measure of leakage is the g-vulnerability, which encompasses several different types of adversaries, with different goals and capabilities. In this paper, we propose a novel approach to perform black-box estimation of the g-vulnerability using ML. A feature of our approach is that it does not require to estimate the conditional probabilities, and that it is suitable for a large class of ML algorithms. First, we formally show the learnability for all data distributions. Then, we evaluate the performance via various experiments using k-Nearest Neighbors and Neural Networks. Our results outperform the frequentist approach when the observables domain is large.

The project management field has the imperative to increase the project probability of success. Experts have developed several project management maturity models to assets and improve the project outcome. However, the current literature lacks of models allowing correlating the measured maturity and the expected probability of success. This paper uses the characteristics of Bayesian networks to formalize experts' knowledge and to extract knowledge from a project overcost database. It develops a method to estimate the impact of project management maturity on the risk of project overcost. A general framework is presented. An industrial case is used to illustrate the application of the method.

SHAP explanations are a popular feature-attribution mechanism for explainable AI. They use game-theoretic notions to measure the influence of individual features on the prediction of a machine learning model. Despite a lot of recent interest from both academia and industry, it is not known whether SHAP explanations of common machine learning models can be computed efficiently. In this paper, we establish the complexity of computing the SHAP explanation in three important settings. First, we consider fully-factorized data distributions, and show that the complexity of computing the SHAP explanation is the same as the complexity of computing the expected value of the model. This fully-factorized setting is often used to simplify the SHAP computation, yet our results show that the computation can be intractable for commonly used models such as logistic regression. Going beyond fully-factorized distributions, we show that computing SHAP explanations is already intractable for a very simple setting: computing SHAP explanations of trivial classifiers over naive Bayes distributions. Finally, we show that even computing SHAP over the empirical distribution is #P-hard.

Machine learning systems are increasingly being used to make impactful decisions such as loan applications and criminal justice risk assessments, and as such, ensuring fairness of these systems is critical. This is often challenging as the labels in the data are biased. This paper studies learning fair probability distributions from biased data by explicitly modeling a latent variable that represents a hidden, unbiased label. In particular, we aim to achieve demographic parity by enforcing certain independencies in the learned model. We also show that group fairness guarantees are meaningful only if the distribution used to provide those guarantees indeed captures the real-world data. In order to closely model the data distribution, we employ probabilistic circuits, an expressive and tractable probabilistic model, and propose an algorithm to learn them from incomplete data. We evaluate our approach on a synthetic dataset in which observed labels indeed come from fair labels but with added bias, and demonstrate that the fair labels are successfully retrieved. Moreover, we show on real-world datasets that our approach not only is a better model than existing methods of how the data was generated but also achieves competitive accuracy.

Artificial intelligence (AI) provides many opportunities to improve private and public life. Discovering patterns and structures in large troves of data in an automated manner is a core component of data science, and currently drives applications in diverse areas such as computational biology, law and finance. However, such a highly positive impact is coupled with significant challenges: how do we understand the decisions suggested by these systems in order that we can trust them? In this report, we focus specifically on data-driven methods -- machine learning (ML) and pattern recognition models in particular -- so as to survey and distill the results and observations from the literature. The purpose of this report can be especially appreciated by noting that ML models are increasingly deployed in a wide range of businesses. However, with the increasing prevalence and complexity of methods, business stakeholders in the very least have a growing number of concerns about the drawbacks of models, data-specific biases, and so on. Analogously, data science practitioners are often not aware about approaches emerging from the academic literature, or may struggle to appreciate the differences between different methods, so end up using industry standards such as SHAP. Here, we have undertaken a survey to help industry practitioners (but also data scientists more broadly) understand the field of explainable machine learning better and apply the right tools. Our latter sections build a narrative around a putative data scientist, and discuss how she might go about explaining her models by asking the right questions.

Finding objects is essential for almost any daily-life visual task. Saliency models have been useful to predict fixation locations in natural images, but are static, i.e., they provide no information about the time-sequence of fixations. Nowadays, one of the biggest challenges in the field is to go beyond saliency maps to predict a sequence of fixations related to a visual task, such as searching for a given target. Bayesian observer models have been proposed for this task, as they represent visual search as an active sampling process. Nevertheless, they were mostly evaluated on artificial images, and how they adapt to natural images remains largely unexplored. Here, we propose a unified Bayesian model for visual search guided by saliency maps as prior information. We validated our model with a visual search experiment in natural scenes recording eye movements. We show that, although state-of-the-art saliency models perform well in predicting the first two fixations in a visual search task, their performance degrades to chance afterward. This suggests that saliency maps alone are good to model bottom-up first impressions, but are not enough to explain the scanpaths when top-down task information is critical. Thus, we propose to use them as priors of Bayesian searchers. This approach leads to a behavior very similar to humans for the whole scanpath, both in the percentage of target found as a function of the fixation rank and the scanpath similarity, reproducing the entire sequence of eye movements.

The tetrad constraint is a condition of which the satisfaction signals a rank reduction of a covariance submatrix and is used to design causal discovery algorithms that detects the existence of latent (unmeasured) variables, such as FOFC. Initially such algorithms only work for cases where the measured and latent variables are all Gaussian and have linear relations (Gaussian-Gaussian Case). It has been shown that a unidimentional latent variable model implies tetrad constraints when the measured and latent variables are all binary (Binary-Binary case). This paper proves that the tetrad constraint can also be entailed when the measured variables are of mixed data types and when the measured variables are discrete and the latent common causes are continuous, which implies that any clustering algorithm relying on this constraint can work on those cases. Each case is shown with an example and a proof. The performance of FOFC on mixed data is shown by simulation studies and is compared with some algorithms with similar functions.