This course will be your guide to learning how to use the power of theory, math and python to create linear regression and logistic regression, two of most popular and useful machine learning models from scratch. This course is designed for folks with some programming experience or experienced developers looking to make the jump to data science and machine learning, I'll teach you how to dive deep into the math behind the linear models in an easy and understandable way. Once, you have understood the inner workings of the linear models and uncovered the black box, you are ready to code everything from the ground up without using any fancy ready made machine learning libraries and yes you will be taught that too! The course is beneficial for understanding the machine learning concepts deeply rather than just using some library to get results, it will guide you in the right direction for learning many other machine learning and deep learning algorithms, as this course covers all the basics required, you will be well on your way to becoming an expert Data Scientist! Since this course goes deep into the math and has coding from scratch, a basic to intermediate knowledge of coding is a must, also good idea of derivatives(calculus), linear algebra(matrix multiplication) and basic probability is required to get the full out of this course.

We will first import libraries as NumPy, matplotlib, pyplot and derivative function. Then with a NumPy function – linspace() we define our variable \(w \) domain between 1.0 and 5.0 and 100 points. Also we define alpha which will represent learning rate. Next, we will define our \(y \) ( in our case \(J(w) \)) and plot to see a convex function, we will use \((w-3) 2 \). So we can see that we plotted our convex function as an example.

I identify as a Machine Learning and Artificial Intelligence enthusiast who is quite fond of making use of data and patterns to develop insights and analysis. In my opinion, Machine learning is where the computational and algorithmic skills of data science meets the statistical thinking of data science. The result is a collection of approaches that requires effective theory as much as effective computation. There are a plethora of machine learning model, with each of them working best for different problems. As such, I believe understanding the problem setting in machine learning is essential to using these tools effectively.

Despite its technological benefits, Internet of Things (IoT) has cyber weaknesses due to the vulnerabilities in the wireless medium. Machine learning (ML)-based methods are widely used against cyber threats in IoT networks with promising performance. Advanced persistent threat (APT) is prominent for cybercriminals to compromise networks, and it is crucial to long-term and harmful characteristics. However, it is difficult to apply ML-based approaches to identify APT attacks to obtain a promising detection performance due to an extremely small percentage among normal traffic. There are limited surveys to fully investigate APT attacks in IoT networks due to the lack of public datasets with all types of APT attacks. It is worth to bridge the state-of-the-art in network attack detection with APT attack detection in a comprehensive review article. This survey article reviews the security challenges in IoT networks and presents the well-known attacks, APT attacks, and threat models in IoT systems. Meanwhile, signature-based, anomaly-based, and hybrid intrusion detection systems are summarized for IoT networks. The article highlights statistical insights regarding frequently applied ML-based methods against network intrusion alongside the number of attacks types detected. Finally, open issues and challenges for common network intrusion and APT attacks are presented for future research.

Many scientific problems focus on observed patterns of change or on how to design a system to achieve particular dynamics. Those problems often require fitting differential equation models to target trajectories. Fitting such models can be difficult because each evaluation of the fit must calculate the distance between the model and target patterns at numerous points along a trajectory. The gradient of the fit with respect to the model parameters can be challenging. Recent technical advances in automatic differentiation through numerical differential equation solvers potentially change the fitting process into a relatively easy problem, opening up new possibilities to study dynamics. However, application of the new tools to real data may fail to achieve a good fit. This article illustrates how to overcome a variety of common challenges, using the classic ecological data for oscillations in hare and lynx populations. Models include simple ordinary differential equations (ODEs) and neural ordinary differential equations (NODEs), which use artificial neural networks to estimate the derivatives of differential equation systems. Comparing the fits obtained with ODEs versus NODEs, representing small and large parameter spaces, and changing the number of variable dimensions provide insight into the geometry of the observed and model trajectories. To analyze the quality of the models for predicting future observations, a Bayesian-inspired preconditioned stochastic gradient Langevin dynamics (pSGLD) calculation of the posterior distribution of predicted model trajectories clarifies the tendency for various models to underfit or overfit the data. Coupling fitted differential equation systems with pSGLD sampling provides a powerful way to study the properties of optimization surfaces, raising an analogy with mutation-selection dynamics on fitness landscapes.

Recently, federated learning has emerged as a promising approach for training a global model using data from multiple organizations without leaking their raw data. Nevertheless, directly applying federated learning to real-world tasks faces two challenges: (1) heterogeneity in the data among different organizations; and (2) data noises inside individual organizations. In this paper, we propose a general framework to solve the above two challenges simultaneously. Specifically, we propose using distributionally robust optimization to mitigate the negative effects caused by data heterogeneity paradigm to sample clients based on a learnable distribution at each iteration. Additionally, we observe that this optimization paradigm is easily affected by data noises inside local clients, which has a significant performance degradation in terms of global model prediction accuracy. To solve this problem, we propose to incorporate mixup techniques into the local training process of federated learning. We further provide comprehensive theoretical analysis including robustness analysis, convergence analysis, and generalization ability. Furthermore, we conduct empirical studies across different drug discovery tasks, such as ADMET property prediction and drug-target affinity prediction.

As a powerful statistical tool that has revolutionized modern molecular evolutionary analysis, Bayesian phylogenetic inference has been widely used for tasks ranging from genomic epidemiology [Dudas et al., 2017, du Plessis et al., 2021] to conservation genetics [DeSalle and Amato, 2004]. Given aligned sequence data (e.g., DNA, RNA or protein sequences) and a model of evolution, Bayesian phylogenetics provides principled approaches to quantify the uncertainty of the evolutionary process in terms of the posterior probabilities of phylogenetic trees [Huelsenbeck et al., 2001]. In addition to uncertainty quantification, Bayesian methods enable integrating out tree uncertainty in order to get more confident estimates of parameters of interest, such as factors in the transmission of Ebolavirus [Dudas et al., 2017]. Bayesian methods also allow complex substitution models [Lartillot and Philippe, 2004], which are important in elucidating deep phylogenetic relationships [Feuda et al., 2017]. Ever since its introduction to the phylogenetic community in the 1990s, Bayesian phylogenetic inference has been dominated by random-walk Markov chain Monte Carlo (MCMC) approaches [Yang and Rannala, 1997, Mau et al., 1999, Huelsenbeck and Ronquist, 2001, Drummond et al., 2002, 2005]. However, this approach is fundamentally limited by the complexities of tree space.

We study the pairwise and mutual independence testing problem for multivariate functional data. Using a basis representation of functional data, we reduce this problem to testing the independence of multivariate data, which may be high-dimensional. For pairwise independence, we apply tests based on distance and Hilbert-Schmidt covariances as well as their marginal versions, which aggregate these covariances for coordinates of random processes. In the case of mutual independence, we study asymmetric and symmetric aggregating measures of pairwise dependence. A theoretical justification of the test procedures is established. In extensive simulation studies and examples based on a real economic data set, we investigate and compare the performance of the tests in terms of size control and power. An important finding is that tests based on distance and Hilbert-Schmidt covariances are usually more powerful than their marginal versions under linear dependence, while the reverse is true under non-linear dependence.

In Machine Learning, we use data and algorithms to build intelligent systems. If you are new to machine learning, you need to work on beginner-level machine learning projects to understand how to use machine learning algorithms on datasets to solve problems. So if you're looking for project ideas as a machine learning beginner, this article is for you. In this article, I'll introduce you to some of the best machine learning project ideas for beginners. Cryptocurrency price prediction is the problem of regression analysis and time series analysis.

L-Softmax proposes a modified softmax classification method to increase the inter-class separability and intra-class compactness.