A Bayesian network, Bayes network, belief network, Bayes(ian) model or probabilistic directed acyclic graphical model is a probabilistic graphical model (a type of statistical model) that represents a set of variables and their conditional dependencies via a directed acyclic graph (DAG). (Wikipedia)
In statistical modeling, we have to calculate the estimator to determine the equation of your model. The problem is, the estimator itself is difficult to calculate, especially when it involves some distributions like Beta, Gamma, or even Gompertz distribution. Maximum Likelihood Estimator (MLE) is one of many methods to calculate the estimator for those distributions. In this article, I will give you some examples to calculate MLE with the Newton-Raphson method using R. Newton-Raphson method is an iterative procedure to calculate the roots of function f. The goal of this method is to make the approximated result as close as possible with the exact result (that is, the roots of the function).
Naive Bayes is a classification algorithm for binary (two-class) and multiclass classification problems. It is called Naive Bayes or idiot Bayes because the calculations of the probabilities for each class are simplified to make their calculations tractable. Rather than attempting to calculate the probabilities of each attribute value, they are assumed to be conditionally independent given the class value. This is a very strong assumption that is most unlikely in real data, i.e. that the attributes do not interact. Nevertheless, the approach performs surprisingly well on data where this assumption does not hold.
Machine learning (ML) is the study of computer algorithms that improve automatically through experience. It is seen as a subset of artificial intelligence. Machine learning algorithms build a mathematical model based on sample data, known as "training data", in order to make predictions or decisions without being explicitly programmed to do so. Machine learning algorithms are used in a wide variety of applications, such as email filtering and computer vision, where it is difficult or infeasible to develop conventional algorithms to perform the needed tasks. Machine learning is closely related to computational statistics, which focuses on making predictions using computers.
Naïve Bayes is a classification technique that serves as the basis for implementing several classifier modeling algorithms. Naïve Bayes-based classifiers are considered some of the simplest, fastest, and easiest-to-use machine learning techniques, yet are still effective for real-world applications. Naïve Bayes is based on Bayes' theorem, formulated by 18th-century statistician Thomas Bayes. This theorem assesses the probability that an event will occur based on conditions related to the event. For example, an individual with Parkinson's disease typically has voice variations; hence such symptoms are considered related to the prediction of a Parkinson's diagnosis.
A Machine Learning interview calls for a rigorous interview process where the candidates are judged on various aspects such as technical and programming skills, knowledge of methods and clarity of basic concepts. If you aspire to apply for machine learning jobs, it is crucial to know what kind of interview questions generally recruiters and hiring managers may ask. This is an attempt to help you crack the machine learning interviews at major product based companies and start-ups. Usually, machine learning interviews at major companies require a thorough knowledge of data structures and algorithms. In the upcoming series of articles, we shall start from the basics of concepts and build upon these concepts to solve major interview questions. Machine learning interviews comprise of many rounds, which begin with a screening test. This comprises solving questions either on the white-board, or solving it on online platforms like HackerRank, LeetCode etc. Here, we have compiled a list of ...
Naive Bayes is a classification algorithm that works based on the Bayes theorem. Before explaining about Naive Bayes, first, we should discuss Bayes Theorem. Bayes theorem is used to find the probability of a hypothesis with given evidence. In this, using Bayes theorem we can find the probability of A, given that B occurred. A is the hypothesis and B is the evidence.
Exploratory analysis of time series data can yield a better understanding of complex dynamical systems. Granger causality is a practical framework for analysing interactions in sequential data, applied in a wide range of domains. In this paper, we propose a novel framework for inferring multivariate Granger causality under nonlinear dynamics based on an extension of self-explaining neural networks. This framework is more interpretable than other neural-network-based techniques for inferring Granger causality, since in addition to relational inference, it also allows detecting signs of Granger-causal effects and inspecting their variability over time. In comprehensive experiments on simulated data, we show that our framework performs on par with several powerful baseline methods at inferring Granger causality and that it achieves better performance at inferring interaction signs. The results suggest that our framework is a viable and more interpretable alternative to sparse-input neural networks for inferring Granger causality.
Approximate Bayesian Computation (ABC) now serves as one of the major strategies to perform model choice and parameter inference on models with intractable likelihoods. An essential component of ABC involves comparing a large amount of simulated data with the observed data through summary statistics. To avoid the curse of dimensionality, summary statistic selection is of prime importance, and becomes even more critical when applying ABC to mechanistic network models. Indeed, while many summary statistics can be used to encode network structures, their computational complexity can be highly variable. For large networks, computation of summary statistics can quickly create a bottleneck, making the use of ABC difficult. To reduce this computational burden and make the analysis of mechanistic network models more practical, we investigated two questions in a model choice framework. First, we studied the utility of cost-based filter selection methods to account for different summary costs during the selection process. Second, we performed selection using networks generated with a smaller number of nodes to reduce the time required for the selection step. Our findings show that computationally inexpensive summary statistics can be efficiently selected with minimal impact on classification accuracy. Furthermore, we found that networks with a smaller number of nodes can only be employed to eliminate a moderate number of summaries. While this latter finding is network specific, the former is general and can be adapted to any ABC application.
Predictive uncertainty estimation is an essential next step for the reliable deployment of deep object detectors in safety-critical tasks. In this work, we focus on estimating predictive distributions for bounding box regression output with variance networks. We show that in the context of object detection, training variance networks with negative log likelihood (NLL) can lead to high entropy predictive distributions regardless of the correctness of the output mean. We propose to use the energy score as a non-local proper scoring rule and find that when used for training, the energy score leads to better calibrated and lower entropy predictive distributions than NLL. We also address the widespread use of non-proper scoring metrics for evaluating predictive distributions from deep object detectors by proposing an alternate evaluation approach founded on proper scoring rules. Using the proposed evaluation tools, we show that although variance networks can be used to produce high quality predictive distributions, adhoc approaches used by seminal object detectors for choosing regression targets during training do not provide wide enough data support for reliable variance learning. We hope that our work helps shift evaluation in probabilistic object detection to better align with predictive uncertainty evaluation in other machine learning domains. Deep object detectors are being increasingly deployed as perception components in safety critical robotics and automation applications. For reliable and safe operation, subsequent tasks using detectors as sensors require meaningful predictive uncertainty estimates correlated with their outputs. As an example, overconfident incorrect predictions can lead to non-optimal decision making in planning tasks, while underconfident correct predictions can lead to under-utilizing information in sensor fusion. This paper investigates probabilistic object detectors, extensions of standard object detectors that estimate predictive distributions for output categories and bounding boxes simultaneously. This paper aims to identify the shortcomings of recent trends followed by state-of-the-art probabilistic object detectors, and proposes to provide theoretically founded solutions for identified issues.