Indian Institute of Technology Gandhinagar ’s Post

🌸 #ProbabilityStatistics #Particularinterest 📜 Some Theoretical and Computational Aspects of the Truncated Multivariate Skew-Normal/Independent Distributions 📍 https://buff.ly/4cj00mQ #marginal_distribution; #Monte_Carlo_integration; #multivariate skew-normal/independent distributions; #random_vector; #truncated_distribution #MDPIOpenAccess #ComSciMathMdpi #MathematicsMdpi

🌸 #ProbabilityStatistics #Particularinterest 📜 Some Theoretical and Computational Aspects of the Truncated Multivariate Skew-Normal/Independent Distributions 📍 https://buff.ly/4cj00mQ #marginal_distribution; #Monte_Carlo_integration; #multivariate skew-normal/independent distributions; #random_vector; #truncated_distribution #MDPIOpenAccess #ComSciMathMdpi #MathematicsMdpi

✳️ 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? 🐎

Key differences between directed and undirected graphs. Directed Graphs: Also known as digraphs, are structures where edges have a specific direction. Think of them as one-way streets in a city, guiding traffic flow from one node to another. In computer science, directed graphs find extensive use in modeling relationships with directionality, such as social networks, website link structures, and network routing. Undirected Graphs: Undirected graphs are more like two-way streets, where edges lack directionality. These graphs represent symmetric relationships, where the connection between nodes is bidirectional. Undirected graphs are pivotal in various domains, including transportation networks, molecular structures, and social connections without inherent directionality. Want to explore more? Check-out the detailed solutions provided in the PDF attached to this post and elevate your understanding of graphs to new heights! Follow me for more such posts. #Interviewprep #datascience #dsa #directedgraphs #undirectedgraphs

Hyperbolic clustering paper that I want to find some time to read: https://lnkd.in/g8dpvmtU

📣 Find our recently published article here! #callforreading #paticularinterested 📑Title: A Bellman–Ford Algorithm for the Path-Length-Weighted Distance in Graphs ✨ Keywords: #graph; #distance; #Bellman_Ford; #algorithm; #path_length_weighted 📍 Link: https://buff.ly/4emkz3v #Combinatorics #MDPIOpenAccess #ComSciMath_Mdpi

In the early 1500s, someone tried to standardize the measurement of land with the method below. Sixteen representative citizens would be recruited after church to stand in line, toe to heel, and then a rod would be cut to match that length. That “rod” then became the unit of land measurement - 16 feet. This is considered one of the first instances of humans intuiting the concept of arithmetic mean (aka average). It wasn’t until the 1800s that we had a solid notion of what an average really is. Statistics is not intuitive. It must be studied. Statistical reasoning helps a lot in visualizing the real-world implications of computer science concepts. For instance, statistics will help you understand that if you call an api n times in parallel, the latency distribution of your composite call will be different (slower) than the latency distribution of the individual calls.

Module Completion | Skewness and Kurtosis Awarded to MD AYAAZ Issued 28 November 2024, 3:57 PM Issued by AMIGO Course: Computational Statistics (CSIT139)-Semester III Awarded for successfully completing the Module - Skewness and Kurtosis Criteria ALL of the following activities are completed: "1.1.1 Introduction to Skewness" "1.1.2 Application of Skewness" "1.1.3 Personian Measure of Skewness" "1.1.4 Bowley's Measure of Skewness" "2.1.1 Introduction to Kurtosis" "2.1.2 Application of Kurtosis" "2.1.3 Introduction to Moments " "2.1.4 Factorial Moments" "2.1.5 Shephard's Correction for Moments" "2.1.6 Skewness Using Moments" "2.1.7 Kurtosis Using Moments" "3rd Module Assessment"

"Temporal Graph ODEs for Irregularly-Sampled Time Series" by Alessio Gravina, Daniele Zambon, Davide Bacciu, Cesare Alippi "Modern graph representation learning works mostly under the assumption of dealing with regularly sampled temporal graph snapshots, which is far from realistic, e.g., social networks and physical systems are characterized by continuous dynamics and sporadic observations. To address this limitation, we introduce the Temporal Graph Ordinary Differential Equation (TG-ODE) framework, which learns both the temporal and spatial dynamics from graph streams where the intervals between observations are not regularly spaced. We empirically validate the proposed approach on several graph benchmarks, showing that TG-ODE can achieve state-of-the-art performance in irregular graph stream tasks." Paper: https://lnkd.in/eXr7QKpm #machinelearning

Together with Alessandro Mazzoccoli and Pierluigi Vellucci, we are excited to share our latest paper: "Refining Heisenberg’s principle: A greedy approximation of step functions with triangular waveform dictionaries". It has just been published in a special issue of Mathematics and Computers in Simulation regarding recent methods for economics, finance, and other social sciences. This paper follows up on our previous paper titled "A solution for the greedy approximation of a step function with a waveform dictionary", published in Communications in Nonlinear Science and Numerical Simulation, where we developed a novel approach for signal analysis that performs especially well when signals are characterized by an unspecified number of jump discontinuities. In our latest paper, we address the case when there are no discontinuities, make gains in efficiency and provide a fast algorithm to extract signals from noisy processes. We show that our method can flexibly adapt to complicated structural changes in a signal via simulation. Due to its localization properties, we take our method to US Real GDP data and affirm post-WW2 volatility followed by a shift into a period of stability past the 1980's. 🔗 Feel free to reach out for discussion! You may access the full paper here: https://lnkd.in/g_SqAmtC #GreedyAlgorithm #WaveformDictionary #StepFunctions #HeisenbergPrinciple #SignalAnalysis #Simulation