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Hello, here is an interactive JFET graph (ID vs VGS) I created using Desmos. You can enter the specifications of the JFET and watch the values change as you vary gate voltage and source resistance. https://lnkd.in/gXADUF8c

Powerful graphing calculators can provide potent math problem solving advantages for students that know how to use–and can afford–them. What is the impact, then, when everyone has free access to leading edge calculation tools? Mike Bergin and I invited educator Kyle Terracciano, Ed.M. to explore using the Desmos calculator in digital testing. https://lnkd.in/ePmr9jC8

Hello LinkedIn Community, project1:Iris Flower Classification Here is my first Machine Learning project done at Luminar Technolab where I've developed an iris flower classification model. In this project, I've used Supervised Machine Learning Algorithm. Iris flower is classified into different species such as setosa,versicolor and virginica based on their sepal and petal measurements. steps implemented: 1]Importing dataset and creating data frame 2]Data preparation 3]Seperating input and output data 4]Split the data into training and testing data 5]Normalization using Standard scalar 6]Model creation using KNN algorithm 7]Performance evaluation of classification model using confusion matrix, accuracy score and confusionmatrixdisplay IDE:#googlecolab Dataset Source:#kaggle Guide:#Sabir,Seban Christo

✳️ Slutsky Theorem The hidden Workhorse 🐎 of asymptotic statistical inference. 📈 This Theorem is a fundamental result in asymptotic statistics. As you already know it is used to justify convergence properties of random variables and is often applied without being mentioned at all. 🎯 Let us recap the statement: Let Xn and Yn be sequences of random variables. Assume the following for n infinitely large: 1️⃣ Xn --d--> X (convergence in distribution) 2️⃣ Yn --p--> c (convergence in probability to a constant c) Then we have the following results: ✅ Xn + Yn --> X + c ✅ XnYn --> cX ✅ Xn / Yn --> X/c if c <> 0 Why is Slutsky very important in statistics? 🔸 Well, it allows you to replace population parameters like σ with consistent estimators i.e. Sn. 🔸The hidden hero is always applied implicitly. Consider the famous t statistic depicted in the attached figure used for hypothesis testing and for building confidence intervals. There are many other examples where the Slutsky theorem is implicitly applied. Can you mention other use cases of the hidden hero? 🐎

Exploring Mixture Models with EM and Nelder-Mead Algorithms 🧠 We often rely on the Expectation-Maximization (EM) algorithm for Gaussian Mixture Models (GMMs), and for good reason – it's efficient and widely used! But in this brief study, I wanted to highlight that EM isn't the only option. While EM excels in many scenarios, the Nelder-Mead Simplex method also performs well in mixture modeling. ⚙️ Check out the code below! 👇 https://lnkd.in/e2QDFJ_8 I’m excited to explore further how these algorithms can be applied to real-world data and different types of distributions. Always learning, always optimizing! 🔧 #DataScience #MachineLearning #MixtureModels #EMAlgorithm #NelderMead #GaussianMixtureModels #Optimization #ParameterEstimation

𝐀𝐥𝐠𝐞𝐛𝐫𝐚, 𝐟𝐫𝐨𝐦 𝐄𝐧𝐜𝐨𝐝𝐢𝐧𝐠 𝐭𝐨 𝐒𝐭𝐚𝐭𝐢𝐬𝐭𝐢𝐜𝐬 𝟐.𝟖𝟓: Encoding data often adds redundancy. The Reed-Muller code is an error-correcting code, constructed using polynomials with coefficients derived from the encoded data. This is useful in communication systems and data storage. In the field of algebra, polynomials and related structures are analyzed through rings and ideals, which are in turn connected to networks of edges and vertices (called graphs). Binomial edge ideals, created from the difference of two terms corresponding to an edge of a graph, is an example of this connection and is relevant in the study of conditional independence in statistics. In this article, the authors have studied the invariant called the 'v-number' of binomial edge ideals and its relation to the Castelnuovo-Mumford regularity of these ideals. The invariant ‘v-number’ plays a significant role in the study of Reed-Muller codes. These are also important in the study of complexity. Read more here: https://lnkd.in/gyXFP_v8 #IITGNResearchSnips #Research #IITGNResearchers Indranath Sengupta Siddhi Balu Ambhore

Why alpha=2 is the ideal state of a NN layer ? In our upcoming monograph, A SemiEmpirical Theory of (Deep) Learning, we show that the weightwatcher HTSR metrics can be derived as a phenomenological Effective Hamiltonian, but one that is governed by a scale-invariant partition function, just like the scale invariance in the Wilson Renormalization Group (RG). And, of course, the RG equations apply near or at the critical point or phase boundary, and are characterized by a critical, universal power-law exponent. And this is exactly what we observe empirically. Both the universal exponent, alpha=2, *and* the signature of scale invariance (the detX condition). And you can observe it too! pip install weightwatcher import weightwatcher as ww watcher = ww.WeightWatcher(model='your model or model folder') details = watcher.analyze(plot=True, detX=True) Check out the blog for more details on how you yourself can check for scale-invariant behavior in your own NN layers: https://lnkd.in/gRnDJzg3 Want to learn more ? Check out: https://weightwatcher.ai and if you want to see the 'proof' or just learn more about weightwatcher, join our Community Discord server. #talkToChuck #theAIguy

📃Scientific paper: Multiclass ROC Abstract: Model evaluation is of crucial importance in modern statistics application. The construction of ROC and calculation of AUC have been widely used for binary classification evaluation. Recent research generalizing the ROC/AUC analysis to multi-class classification has problems in at least one of the four areas: 1. failure to provide sensible plots 2. being sensitive to imbalanced data 3. unable to specify mis-classification cost and 4. unable to provide evaluation uncertainty quantification. Borrowing from a binomial matrix factorization model, we provide an evaluation metric summarizing the pair-wise multi-class True Positive Rate (TPR) and False Positive Rate (FPR) with one-dimensional vector representation. Visualization on the representation vector measures the relative speed of increment between TPR and FPR across all the classes pairs, which in turns provides a ROC plot for the multi-class counterpart. An integration over those factorized vector provides a binary AUC-equivalent summary on the classifier performance. Mis-clasification weights specification and bootstrapped confidence interval are also enabled to accommodate a variety of of evaluation criteria. To support our findings, we conducted extensive simulation studies and compared our method to the pair-wise averaged AUC statistics on benchmark datasets. Continued on ES/IODE ➡️ https://etcse.fr/c9u ------- If you find this interesting, feel free to follow, comment and share. We need your help to enhance our visibility, so that our platform continues to serve you.

Looking forward to another edition of the two-day course about Linear Mixed Models in R. We are very happy to work together with Joris De Wolf since several years! If you are interested in the next edition, more info on the course: https://shorturl.at/jO148 #technology #training #statistics #linearmixedmodels

The ☆trval is the earthval if we think deep enough, we will interconnect many more analytical Metrics using mathematical variables. We want to focus in on ANALYZING RAM Byte Frequency Streams in (AU) as a means to combine into NANO Spectrum Analytics.