The policy gradient theorem is defined based on an objective with respect to the initial distribution over states. In the discounted case, this results in policies that are optimal for one distribution over initial states, but may not be uniformly optimal for others, no matter where the agent starts from. Furthermore, to obtain unbiased gradient estimates, the starting point of the policy gradient estimator requires sampling states from a normalized discounted weighting of states. However, the difficulty of estimating the normalized discounted weighting of states, or the stationary state distribution, is quite well-known. Additionally, the large sample complexity of policy gradient methods is often attributed to insufficient exploration, and to remedy this, it is often assumed that the restart distribution provides sufficient exploration in these algorithms. In this work, we propose exploration in policy gradient methods based on maximizing entropy of the discounted future state distribution. The key contribution of our work includes providing a practically feasible algorithm to estimate the normalized discounted weighting of states, i.e, the \textit{discounted future state distribution}. We propose that exploration can be achieved by entropy regularization with the discounted state distribution in policy gradients, where a metric for maximal coverage of the state space can be based on the entropy of the induced state distribution. The proposed approach can be considered as a three time-scale algorithm and under some mild technical conditions, we prove its convergence to a locally optimal policy. Experimentally, we demonstrate usefulness of regularization with the discounted future state distribution in terms of increased state space coverage and faster learning on a range of complex tasks.

Explanations in Machine Learning come in many forms, but a consensus regarding their desired properties is yet to emerge. In this paper we introduce a taxonomy and a set of descriptors that can be used to characterise and systematically assess explainable systems along five key dimensions: functional, operational, usability, safety and validation. In order to design a comprehensive and representative taxonomy and associated descriptors we surveyed the eXplainable Artificial Intelligence literature, extracting the criteria and desiderata that other authors have proposed or implicitly used in their research. The survey includes papers introducing new explainability algorithms to see what criteria are used to guide their development and how these algorithms are evaluated, as well as papers proposing such criteria from both computer science and social science perspectives. This novel framework allows to systematically compare and contrast explainability approaches, not just to better understand their capabilities but also to identify discrepancies between their theoretical qualities and properties of their implementations. We developed an operationalisation of the framework in the form of Explainability Fact Sheets, which enable researchers and practitioners alike to quickly grasp capabilities and limitations of a particular explainable method. When used as a Work Sheet, our taxonomy can guide the development of new explainability approaches by aiding in their critical evaluation along the five proposed dimensions.

We will try to build a single neuron network, which can predict the admissions of a graduate school. The data we will use is shared above in google drive. The first 5 rows of data are shown below. The first column admit indicates whether the student is getting admitted to the school or not, this will be the target for our model; the second column gre and the third column gpa are numerical features for the student; the fourth column rank is a categorical feature. We will apply one-hot encoding to the categorical feature to add dummy columns.

Color-based segmentation method has been applied for abnormal area selection. Color and texture features are combined for discrimination of abnormal regions and frames. We compare the segmentation results with the current state-of-the-art methods. Computer-aided diagnosis of gastric diseases from endoscopy frames is an important task. Colors are the basic visual features of endoscopic images and also provide clues about abnormal regions in endoscopy frames.

Demonstrated experience in PySpark is one of the most desirable competencies that employers are looking for when building data science teams, because it enables these teams to own live data products. While I've previously blogged about PySpark, Parallelization, and UDFs, I wanted to provide a proper overview of this topic as a book chapter. I'm sharing this complete chapter, because I want to encourage the adoption of PySpark as a tool for data scientists. All code examples from this post are available here, and all prerequisites are covered in the sample chapters here. You might want to grab some snacks before diving in! Spark is a general-purpose computing framework that can scale to massive data volumes. It builds upon prior big data tools such as Hadoop and MapReduce, while providing significant improvements in the expressivity of the languages it supports. One of the core components of Spark is resilient distributed datasets (RDD), which enable clusters of machines to perform workloads in a coordinated, and fault-tolerant process. In more recent versions of Spark, the Dataframe API provides an abstraction on top of RDDs that resembles the same data structure in R and Pandas. PySpark is the Python interface to Spark, and it provides an API for working with large-scale datasets in a distributed computing environment. PySpark is an extremely valuable tool for data scientists, because it can streamline the process for translating prototype models into production-grade model workflows. At Zynga, our data science team owns a number of production-grade systems that provide useful signals to our game and marketing teams. By using PySpark, we've been able to reduce the amount of support we need from engineering teams to scale up models from concept to production.

Maximizing the (log) likelihood is equivalent to minimizing the binary cross entropy. There is literally no difference between the two objective functions, so there can be no difference between the resulting model or its characteristics. This of course, can be extended quite simply to the multiclass case using softmax cross-entropy and the so-called multinoulli likelihood, so there is no difference when doing this for multiclass cases as is typical in, say, neural networks. The difference between MLE and cross-entropy is that MLE represents a structured and principled approach to modeling and training, and binary/softmax cross-entropy simply represent special cases of that applied to problems that people typically care about. After that aside on maximum likelihood estimation, let's delve more into the relationship between negative log likelihood and cross entropy.

Interpretability is the degree to which a human can understand the cause of a decision – Miller, Tim[1] Explainable AI (XAI) is a sub-field of AI which has been gaining ground in the recent past. And as I machine learning practitioner dealing with customers day in and day out, I can see why. I've been an analytics practitioner for more than 5 years and I swear, the hardest part of a machine learning project is not creating the perfect model which beats all the benchmarks. It's the part where you convince the customer why and how it works. Humans always had a dichotomy when faced with the unknown.

The purpose of this usecase is to formulate inferences and generate insights based on certain indicators like the bed occupancy status, ward-wise revenues, delivery procedures (normal or caesarian), revenues generated by doctors, etc. The analysis performed gave deep insights (yearly, monthly, weekly) into the number of outpatients getting converted to inpatients, ward-wise inputs on bed occupancy and revenues, doctors' performance and the revenues generated by them, type of delivery (normal or caesarian), etc. This usecase also tries to predict the weekly trends in the patients which will help for better monitoring and allotment of resources. To know how Qualetics gives an effective solution, download the full usecase.

The last decades have not only been characterized by an explosive growth of data, but also an increasing appreciation of data as a valuable resource. It's value comes with the ability to extract meaningful patterns that are of economic, societal or scientific relevance. A particular challenge is to identify patterns across time, including patterns that might only become apparent when the temporal dimension is taken into account. Here, we present a novel method that aims to achieve this by detecting dynamic clusters, i.e. structural elements that can be present over prolonged durations. It is based on an adaptive identification of majority overlaps between groups at different time points and allows the accommodation of transient decompositions in otherwise persistent dynamic clusters. As such, our method enables the detection of persistent structural elements with internal dynamics and can be applied to any classifiable data, ranging from social contact networks to arbitrary sets of time stamped feature vectors. It provides a unique tool to study systems with non-trivial temporal dynamics with a broad applicability to scientific, societal and economic data.

Tropical Geometry and Mathematical Morphology share the same max-plus and min-plus semiring arithmetic and matrix algebra. In this chapter we summarize some of their main ideas and common (geometric and algebraic) structure, generalize and extend both of them using weighted lattices and a max-$\star$ algebra with an arbitrary binary operation $\star$ that distributes over max, and outline applications to geometry, machine learning, and optimization. Further, we generalize tropical geometrical objects using weighted lattices. Finally, we provide the optimal solution of max-$\star$ equations using morphological adjunctions that are projections on weighted lattices, and apply it to optimal piecewise-linear regression for fitting max-$\star$ tropical curves and surfaces to arbitrary data that constitute polygonal or polyhedral shape approximations. This also includes an efficient algorithm for solving the convex regression problem of data fitting with max-affine functions.