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
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𝐆𝐚𝐮𝐬𝐬𝐢𝐚𝐧 𝐏𝐫𝐨𝐜𝐞𝐬𝐬 𝐑𝐞𝐠𝐫𝐞𝐬𝐬𝐢𝐨𝐧 I recently came across a helpful and simple tutorial for Gaussian Process Regression (GPR) that I wanted to share to who want to start learning it. "An Intuitive Tutorial to Gaussian Process Regression" by Jie Wang from the University of Waterloo provides a clear and accessible introduction to this powerful machine learning technique. The tutorial covers key concepts like multivariate Gaussians, kernels, and non-parametric models, and includes useful visualizations to illustrate ideas. If you're interested in learning about GPR, I recommend checking out the full PDF at https://lnkd.in/g6_Cxjxa. The code examples are available on GitHub as well: https://lnkd.in/gtwQ8K2j Let me know if you find it helpful! #GaussianProcessRegression #MachineLearning #Regression #BayesianMethods #Kernels #NonParametricModels #DataScience #Statistics #Probability #Tutorial
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Implemented 𝐒𝐨𝐟𝐭𝐦𝐚𝐱 𝐑𝐞𝐠𝐫𝐞𝐬𝐬𝐢𝐨𝐧 (𝐌𝐮𝐥𝐭𝐢𝐧𝐨𝐦𝐢𝐚𝐥 𝐋𝐨𝐠𝐢𝐬𝐭𝐢𝐜 𝐑𝐞𝐠𝐫𝐞𝐬𝐬𝐢𝐨𝐧) from scratch with 𝑵𝒖𝒎𝒑𝒚 on the Iris dataset. Tackled gradient descent, both without any regularization and with 𝒍2 ( 𝑹𝒊𝒅𝒈𝒆) 𝒓𝒆𝒈𝒖𝒍𝒂𝒓𝒊𝒛𝒂𝒕𝒊𝒐𝒏. Learned a ton about translating mathematical equations into Numpy from scratch. 🙂 𝐉𝐮𝐩𝐲𝐭𝐞𝐫 𝐥𝐚𝐛: https://lnkd.in/dMtn_RKX 𝐌𝐲 𝐧𝐨𝐭𝐞𝐬: https://lnkd.in/duAAxAVv
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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
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I am thrilled to announce that I have successfully completed a course on Algorithm on Graphs! This intensive course has deepened my understanding of various graph algorithms, including but not limited to: Breadth-First Search (BFS) and Depth-First Search (DFS) Shortest Path Algorithms (Dijkstra's, Bellman-Ford) Minimum Spanning Tree (Prim's, Kruskal's) Network Flow Algorithms Strongly Connected Components The knowledge gained from this course will be invaluable in solving complex problems and optimizing solutions in my future projects.I am eager to apply these skills in real-world scenarios and continue my journey in the field of algorithms and data structures. #Algorithms #Graphs #Learning #ProfessionalDevelopment #ContinuousImprovement
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🚀 Day [61] : #100DaysOfDSA 🚀 Today, I tackled some challenging graph problems that required a deep understanding of topological sorting, cycle detection, and traversal techniques. Here’s a quick rundown of the problems and solutions: Course Schedule - I Problem: Determine if all courses can be finished given some prerequisites. Solution: Utilized Kahn’s Algorithm (BFS) for cycle detection. Course Schedule - II Problem: Find the order in which to take courses to finish all. Solution: Implemented topological sort using BFS. Find Eventual Safe States Problem: Identify nodes in a directed graph that lead to terminal nodes. Solution: Reversed graph traversal and topological sorting. Alien Dictionary Problem: Determine the order of characters in an alien language based on dictionary order. Solution: Constructed the graph and performed topological sorting. I am continuously learning and improving my understanding of complex algorithms and data structures. Each problem presents a unique challenge and an opportunity to grow. 💪 Feel free to check out the detailed solutions on my GitHub and drop any suggestions or improvements. Let’s connect and discuss more about algorithms and problem-solving strategies! #DataStructures #Algorithms #GraphTheory #CodingChallenge
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SMOTE (Synthetic Minority Over-sampling Technique) 1. Understanding the Problem: In many classification tasks, datasets may exhibit class imbalance, where one class (the minority class) is underrepresented compared to the other class (the majority class). This class imbalance can lead to biased models that perform poorly in predicting the minority class. 2. SMOTE Overview: SMOTE is a popular technique used to address class imbalance by oversampling the minority class. It works by generating synthetic examples rather than replicating existing minority class samples. 3. How SMOTE Works: Here's a step-by-step explanation of the SMOTE algorithm: a. Identifying Minority Class Instances: SMOTE first identifies the instances belonging to the minority class in the dataset. b. Finding Nearest Neighbors: For each minority class instance, SMOTE calculates the k nearest neighbors (typically using Euclidean distance) in the feature space. These neighbors can be identified using various distance metrics. c. Generating Synthetic Samples: For each minority class instance, SMOTE selects one or more of its k nearest neighbors and creates synthetic examples by interpolating between them. This interpolation is performed in feature space by randomly selecting a point along the line segment joining the minority instance and its selected neighbor(s). d. Repeat for All Minority Instances: This process is repeated for all minority class instances, resulting in an augmented dataset with a balanced class distribution. 4. Pros of SMOTE: + SMOTE effectively mitigates class imbalance issues by oversampling the minority class without replicating existing instances. It helps prevent overfitting that might occur when simply duplicating minority class samples. +SMOTE can improve the generalization capability of classifiers by providing more representative samples of the minority class. 5. Cons of SMOTE: - While SMOTE is effective in many scenarios, it may not perform optimally in situations where the minority class is highly overlapping with the majority class or when there are noisy samples. - The choice of the parameter k (number of nearest neighbors) can impact the performance of SMOTE and should be carefully selected based on the dataset characteristics. #machinelearning #smote #classification #imbalance #datasets #knn
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Greetings, everyone! As we already discuss the core concepts of Gradient Descent in our previous post. Today, I will share the mathematical formulation of Gradient Descent. This notes also involves a brief discussion of the types of Gradient Descent Stay tuned for next topics #MachineLearning #DataScience
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🌟 Day 20/60: DSA Challenge – Exploring the World of Graphs 🌟 🚀 Today’s Achievement: Took a deep dive into the basics of graphs and implemented Dijkstra's Algorithm for finding the shortest path. This marked an exciting step in understanding how graphs can model complex networks. 💡 Key Learnings: Built a solid foundation in graph theory, covering nodes, edges, and weighted graphs. Implemented Dijkstra's Algorithm, appreciating its efficiency in finding optimal paths in weighted graphs. Realized the importance of priority queues in ensuring algorithmic efficiency. 🌟 Why It’s Exciting: Graphs are everywhere—from social networks to navigation systems—and mastering them opens doors to solving real-world challenges. 🎯 Next Steps: Applying these concepts to practical problems and diving deeper into advanced graph algorithms! 🙌 Over to You: How did you first approach Dijkstra’s Algorithm? Any tips for mastering graph theory? Let’s share and grow together! #DSAChallenge #Day20 #GraphTheory #DijkstrasAlgorithm #ProblemSolving #CodingJourney
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Learning About K-Nearest Neighbors (KNN) and Its Hyperparameters Recently explored the K-Nearest Neighbors (KNN) algorithm, a simple yet powerful classification and regression method. KNN predicts a target based on the majority class or average of the 'K' nearest data points. While effective, getting the best out of KNN requires tuning a few key hyperparameters: 1️⃣ K (Number of Neighbors): Determines how many neighbors influence the prediction. A small K makes the model sensitive to noise, while a larger K smooths the decision boundary. 2️⃣ Distance Metric: Defines how distance is measured (e.g., Euclidean, Manhattan). The choice affects how "neighborliness" is calculated, impacting model performance. 3️⃣ Weighting of Neighbors: Allows closer neighbors to have more influence than those farther away. Options like "uniform" (equal weight) or "distance" (weights based on proximity) can improve results. Tuning these parameters can make a significant difference in KNN’s effectiveness. It’s fascinating how a simple algorithm can be so adaptable! #MachineLearning #KNN #Hyperparameters #DataScience
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"Hessian as a regularization term" One of the big challenges with XGBoost is multi-class classification problems. XGBoost is solving an optimization problem using 2nd order Newton Raphson method. In this approach, regression trees as well as binary logistic loss classifiers fit well into the framework because then we are solving using an univariate Taylor series approximation (both gradient as well as hessian are scalars). With multi-class problems using a categorical cross entropy loss function and softmax scoring function, makes it a multivariate Taylor series which requires evaluating expensive inverse Hessian to find node splits, leaf weights etc. This makes it slow. One can use quasi Newton approximation for Hessian inverse but still the number of evaluations are too high. Many people have used only diagonal elements of the Hessian and still got good results. The xgboost algorithm still works if you remove the hessian term from the equation. The hessian term acts as a regularizer. Using full hessian is prohibitively slow. #machinelearning #softwareengineering #datascience #linearalgebra
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