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05:32, 10 June 2025 Thakshashila talk contribs created page Precision-Recall Curve (Created page with "= Precision-Recall Curve = The '''Precision-Recall Curve''' (PR Curve) is a graphical representation used to evaluate the performance of binary classification models, especially on '''imbalanced datasets''' where the positive class is rare. It plots '''Precision''' (y-axis) against '''Recall''' (x-axis) for different classification thresholds. == Why Use Precision-Recall Curve? == In many real-world problems like fraud detection, disease diagnosis, or spam filtering,...")
05:30, 10 June 2025 Thakshashila talk contribs created page Model Evaluation Metrics (Created page with "= Model Evaluation Metrics = '''Model Evaluation Metrics''' are quantitative measures used to assess how well a machine learning model performs. They help determine the accuracy, reliability, and usefulness of models in solving real-world problems. == Importance of Evaluation Metrics == Without evaluation metrics, it's impossible to know whether a model is effective or not. Metrics guide model selection, tuning, and deployment by measuring: * Accuracy of predictions...")
05:29, 10 June 2025 Thakshashila talk contribs created page Classification (Created page with "= Classification = '''Classification''' is a fundamental task in '''machine learning''' and '''data science''' where the goal is to predict discrete labels (categories) for given input data. It is a type of '''supervised learning''' since the model learns from labeled examples. == What is Classification? == In classification, a model is trained on a dataset with input features and known target classes. Once trained, the model can assign class labels to new, unseen dat...")
05:27, 10 June 2025 Thakshashila talk contribs created page ROC Curve (Created page with "= ROC Curve = The '''ROC Curve''' ('''Receiver Operating Characteristic Curve''') is a graphical tool used to evaluate the performance of binary classification models. It plots the '''True Positive Rate (TPR)''' against the '''False Positive Rate (FPR)''' at various threshold settings. == Purpose == The ROC Curve shows the trade-off between sensitivity (recall) and specificity. It helps assess how well a classifier can distinguish between two classes. == Definitions...")
05:26, 10 June 2025 Thakshashila talk contribs created page Micro F1 Score (Created page with "= Micro F1 Score = The '''Micro F1 Score''' is an evaluation metric used primarily in '''multi-class''' and '''multi-label classification''' tasks. Unlike Macro F1 Score, it calculates global counts of true positives, false positives, and false negatives across all classes, then uses these to compute a single Precision, Recall, and F1 Score. It is most useful when the dataset is '''imbalanced''' and you care more about overall performance than per-class fai...")
05:25, 10 June 2025 Thakshashila talk contribs created page Weighted F1 (Created page with "= Weighted F1 Score = The '''Weighted F1 Score''' is a metric used in multi-class classification to evaluate model performance by computing the F1 Score for each class and taking the average, weighted by the number of true instances for each class (i.e., the class "support"). It is especially useful when working with '''imbalanced datasets''', where some classes are more frequent than others. == Definition == :<math> \text{Weighted F1} = \sum_{i=1}^{C} w_i \cdot F1_i...")
05:24, 10 June 2025 Thakshashila talk contribs created page Macro F1 (Created page with "= Macro F1 Score = The '''Macro F1 Score''' is an evaluation metric used in multi-class classification tasks. It calculates the F1 Score independently for each class and then takes the average (unweighted) across all classes. Unlike the regular F1 Score, which is typically applied to binary classification, the Macro F1 is designed for problems involving more than two classes. == Definition == 1. Compute Precision and Recall for each class individually 2. Compute...")
05:23, 10 June 2025 Thakshashila talk contribs created page Complementary metrics (Created page with "= Complementary Metrics in Machine Learning = '''Complementary Metrics''' refer to pairs or groups of evaluation metrics that together provide a more complete and balanced understanding of a classification model’s performance. Because no single metric is perfect, especially in real-world and imbalanced datasets, these metrics are used together to highlight different strengths and weaknesses of a model. == Why Use Complementary Metrics? == Using only one metric like...")
05:22, 10 June 2025 Thakshashila talk contribs created page F1 Score (Created page with "= F1 Score = The '''F1 Score''' is a performance metric used in classification problems that balances the trade-off between Precision and Recall (also known as Sensitivity). It is especially useful when the dataset is imbalanced, and both false positives and false negatives are important. == Definition == The F1 Score is the '''harmonic mean''' of Precision and Recall. :<math> F1 = 2 \cdot \frac{\text{Precision} \cdot \text{Recall}}{\text{Precision} + \te...")
05:21, 10 June 2025 Thakshashila talk contribs created page Specificity (Created page with "= Specificity = '''Specificity''', also known as the '''True Negative Rate (TNR)''', is a performance metric in binary classification tasks. It measures the proportion of actual negative instances that are correctly identified by the model. == Definition == :<math> \text{Specificity} = \frac{TN}{TN + FP} </math> Where: * '''TN''' = True Negatives – actual negatives correctly predicted * '''FP''' = False Positives – actual negatives incorrectly predicted as positi...")
05:20, 10 June 2025 Thakshashila talk contribs created page Sensitivity (Created page with "= Sensitivity = '''Sensitivity''', also known as '''Recall''' or the '''True Positive Rate (TPR)''', is a performance metric used in classification problems. It measures how well a model can identify actual positive instances. == Definition == :<math> \text{Sensitivity} = \frac{TP}{TP + FN} </math> Where: * '''TP''' = True Positives – actual positives correctly predicted * '''FN''' = False Negatives – actual positives incorrectly predicted as negative Sensitivit...")
05:20, 10 June 2025 Thakshashila talk contribs created page Accuracy (Created page with "= Accuracy = '''Accuracy''' is one of the most commonly used metrics to evaluate the performance of a classification model in machine learning. It tells us the proportion of total predictions that were correct. == Definition == :<math> \text{Accuracy} = \frac{TP + TN}{TP + TN + FP + FN} </math> Where: * '''TP''' = True Positives * '''TN''' = True Negatives * '''FP''' = False Positives * '''FN''' = False Negatives Accuracy answers the question: '''"Out of all predict...")
05:18, 10 June 2025 Thakshashila talk contribs created page Recall (Created page with "= Recall = '''Recall''' is a metric used in classification to measure how many of the actual positive instances were correctly identified by the model. It is also known as '''sensitivity''' or the '''true positive rate'''. == Definition == :<math> \text{Recall} = \frac{TP}{TP + FN} </math> Where: * '''TP''' = True Positives – correctly predicted positive instances * '''FN''' = False Negatives – actual positives incorrectly predicted as negative Recall answers th...")
05:18, 10 June 2025 Thakshashila talk contribs created page Precision (Created page with "= Precision = '''Precision''' is a metric used in classification tasks to measure how many of the predicted positive results are actually correct. It is also known as the '''positive predictive value'''. == Definition == :<math> \text{Precision} = \frac{TP}{TP + FP} </math> Where: * '''TP''' = True Positives – correct positive predictions * '''FP''' = False Positives – incorrect positive predictions Precision helps to answer the question: '''"Of all the items la...")
05:13, 10 June 2025 Thakshashila talk contribs created page Confusion Matrix (Created page with "= Confusion Matrix = '''Confusion Matrix''' is a performance measurement tool used in machine learning, particularly for classification problems. It provides a summary of prediction results on a classification problem by comparing the actual labels with those predicted by the model. == What is a Confusion Matrix? == A confusion matrix is a table that describes the performance of a classification model. It shows how many instances were correctly or incorrectly predicte...")
04:22, 5 June 2025 Thakshashila talk contribs created page Neural Network (Created page with "= Neural Network = '''Neural Networks''' are a class of algorithms within Machine Learning and Deep Learning that are designed to recognize patterns. They are inspired by the structure and function of the biological brain and are used to approximate complex functions by learning from data. == Overview == A neural network consists of interconnected units (called '''neurons''' or '''nodes''') organized in layers. These layers process input data through weighted c...")
04:21, 5 June 2025 Thakshashila talk contribs created page Data Science (Created page with "= Data Science = '''Data Science''' is an interdisciplinary field that uses scientific methods, algorithms, and systems to extract knowledge and insights from structured and unstructured data. It integrates techniques from statistics, computer science, and domain-specific knowledge to turn raw data into actionable intelligence. == Overview == Data Science combines aspects of data analysis, machine learning, data engineering, and software development to address complex...")
04:20, 5 June 2025 Thakshashila talk contribs created page Deep Learning (Created page with "= Deep Learning = '''Deep Learning''' is a subfield of Machine Learning concerned with algorithms inspired by the structure and function of the brain, known as artificial neural networks. It is at the heart of many recent advances in Artificial Intelligence. == Overview == Deep learning models automatically learn representations of data through multiple layers of abstraction. These models excel at recognizing patterns in unstructured data such as images, audio,...")
04:20, 5 June 2025 Thakshashila talk contribs created page Artificial Intelligence (Created page with "= Artificial Intelligence = '''Artificial Intelligence (AI)''' is a branch of computer science that aims to create systems or machines that exhibit behavior typically requiring human intelligence. These behaviors include learning, reasoning, problem-solving, perception, language understanding, and decision-making. == Overview == Artificial Intelligence involves the design and development of algorithms that allow computers and software to perform tasks that would normal...")
04:18, 5 June 2025 Thakshashila talk contribs created page What is Machine Learning (Created page with "= What is Machine Learning = '''Machine Learning (ML)''' is a subfield of artificial intelligence (AI) that focuses on the development of systems that can learn from data and improve their performance over time without being explicitly programmed. == Overview == Machine Learning allows computers to recognize patterns, make decisions, and predict outcomes based on historical data. It contrasts with traditional programming, where rules and logic are manually coded. == T...")
04:54, 24 May 2025 Thakshashila talk contribs created page Problem: Find (A ∩ B) × (B ∩ C) (Created page with "= Problem: Find (A ∩ B) × (B ∩ C) = Given sets: <math>A = \{3, 5, 7\}</math> <math>B = \{7, 8\}</math> <math>C = \{8, 9\}</math> == Step 1: Find the Intersection A ∩ B == Intersection means elements common to both sets. Elements of A: 3, 5, 7 Elements of B: 7, 8 Common element is: <math>A \cap B = \{7\}</math> == Step 2: Find the Intersection B ∩ C == Elements of B: 7, 8 Elements of C: 8, 9 Common element is: <math>B \cap C = \{8\}</mat...")
04:54, 24 May 2025 Thakshashila talk contribs deleted page Problem 1 (content was: "= Problem: Find<math> \((A \cap B) \times (B \cap C)\)</math> = Given sets: <math> A = \{3, 5, 7\} \\ B = \{7, 8\} \\ C = \{8, 9\} </math> == Step 1: Find the Intersection \(A \cap B\) == The intersection of two sets contains all elements common to both sets. * Elements of \(A\) are: 3, 5, 7 * Elements of \(B\) are: 7, 8 Common elements: <math>A \cap...", and the only contributor was "Thakshashila" (talk))
04:53, 24 May 2025 Thakshashila talk contribs created page Problem 1 (Created page with "= Problem: Find \((A \cap B) \times (B \cap C)\) = Given sets: <math> A = \{3, 5, 7\} \\ B = \{7, 8\} \\ C = \{8, 9\} </math> == Step 1: Find the Intersection \(A \cap B\) == The intersection of two sets contains all elements common to both sets. * Elements of \(A\) are: 3, 5, 7 * Elements of \(B\) are: 7, 8 Common elements: <math>A \cap B = \{7\}</math> == Step 2: Find the Intersection \(B \cap C\) == * Elements of \(B\) are: 7, 8 * Elements of \(C\) are:...")
04:47, 24 May 2025 Thakshashila talk contribs created page Ahmed Zewail (Created page with "= Ahmed Zewail - The Father of Femtochemistry = '''Ahmed Hassan Zewail''' (1946–2016) was an Egyptian-American scientist known as the Father of Femtochemistry. He won the '''Nobel Prize in Chemistry''' in 1999 for his pioneering work on observing chemical reactions at extremely fast timescales. == Early Life and Education == * Born in Damanhur, Egypt, in 1946 * Studied at Alexandria University in Egypt * Completed his PhD at the University of Pennsylvania, USA...")
04:46, 24 May 2025 Thakshashila talk contribs created page Antoine Lavoisier (Created page with "= Antoine Lavoisier - The Father of Modern Chemistry = '''Antoine Laurent Lavoisier''' (1743–1794) was a French chemist who is widely regarded as the Father of Modern Chemistry. He revolutionized chemistry by introducing a scientific and quantitative approach to studying matter and chemical reactions. == Early Life and Education == * Born in Paris, France, in 1743 * Educated in science and law, but devoted his life to chemistry * Known for using careful measurem...")
04:44, 24 May 2025 Thakshashila talk contribs created page Marie Curie (Created page with "= Marie Curie - The Pioneer of Radioactivity = '''Marie Curie''' (1867–1934) was a world-renowned scientist known for her groundbreaking work on '''radioactivity'''. She was the first woman to win a Nobel Prize, and the only person to win Nobel Prizes in two different scientific fields — Physics and Chemistry. == Early Life and Education == * Born as '''Maria Sklodowska''' in Warsaw, Poland (1867) * Moved to Paris to study at the University of Paris (Sorbonne)...")
04:29, 24 May 2025 Thakshashila talk contribs created page Category:Chemistry (Created page with "= What is Chemistry? - Definition, Explanation, and Importance = '''Chemistry''' is the branch of science that studies the '''composition''', '''structure''', '''properties''', and '''changes of matter'''. It helps us understand how substances interact, combine, and change to form new substances. == Definition == Chemistry is the scientific study of: * What matter is made of (elements, atoms, molecules) * How substances behave and interact * How new materials are form...")
04:28, 24 May 2025 Thakshashila talk contribs created page Category:Mathematics (Created page with "= What is Mathematics? - Definition, Explanation, and Importance = '''Mathematics''' is the science of numbers, shapes, patterns, and logical reasoning. It helps us solve problems in daily life, science, business, and technology. == Definition == Mathematics is the study of: * '''Numbers''' and their operations (like addition, subtraction) * '''Shapes''' and space (geometry) * '''Patterns''' and sequences (algebra) * '''Measurements''' and quantities * '''Logical thin...")
04:27, 24 May 2025 Thakshashila talk contribs created page Category:Physics (Created page with "= What is Physics? - Definition, Explanation, and Importance = '''Physics''' is the branch of science that deals with the study of the '''natural world''', focusing on the '''matter''', '''energy''', and the '''laws that govern their behavior''. It tries to answer questions like: * How do objects move? * Why do things fall? * What is light? * How is electricity generated? * What causes sound? == Definition == Physics is the scientific study of '''matter''', '''energy...")
04:24, 24 May 2025 Thakshashila talk contribs created page Cartesian Product (Created page with "= Cartesian Product - Definition, Explanation, and Examples = The '''Cartesian Product''' is an operation used in mathematics to combine two sets and form a new set made of ordered pairs. This concept is widely used in set theory, coordinate geometry, and computer science. == Definition == If <math>A</math> and <math>B</math> are two sets, the '''Cartesian product''' of <math>A</math> and <math>B</math> is the set of all ordered pairs where: - The first element is fr...")
04:22, 24 May 2025 Thakshashila talk contribs created page Cartesian Product of Two Sets (Created page with "= Cartesian Product of Two Sets - Definition and Step-by-Step Examples = The [[Cartesian Product]] of two sets is the set of all possible '''ordered pairs''' where the first element comes from the first set and the second element comes from the second set. == Definition == If <math>A</math> and <math>B</math> are two sets, then the Cartesian Product of <math>A</math> and <math>B</math>, denoted by <math>A \times B</math>, is defined as: <math> A \times B...")
04:18, 24 May 2025 Thakshashila talk contribs created page Ordered Pairs in set (Created page with "= Ordered Pairs - Definition and Examples = An '''ordered pair''' is a fundamental concept in mathematics used to represent two elements together with an order that matters. It is usually written as <math>(a, b)</math>, where <math>a</math> is called the '''first element''' and <math>b</math> is the '''second element'''. == Key Points == * Unlike sets, the order of elements in an ordered pair is important. * Two ordered pairs <math>(a, b)</math> and <math>(c, d)</ma...")
04:16, 24 May 2025 Thakshashila talk contribs created page De Morgan (Created page with "= Augustus De Morgan - Mathematician Behind De Morgan's Laws = '''Augustus De Morgan''' (1806–1871) was a British mathematician and logician known for his pioneering work in formalizing logic and mathematics. He is famous for formulating the laws that bear his name, called De Morgan's Laws, which are fundamental in set theory, logic, and computer science. == Early Life and Education == - Born in India in 1806, De Morgan moved to England at a young age. - H...")
04:15, 24 May 2025 Thakshashila talk contribs created page De Morgan’s Laws (Created page with "= De Morgan's Laws - Definition, Explanation, and Examples = '''De Morgan''''s laws are fundamental rules in set theory that describe the relationship between union, intersection, and complements of sets. They help simplify complex set expressions, especially involving complements. == Statements of De Morgan's Laws == Let <math>A</math> and <math>B</math> be two sets and <math>U</math> be the universal set. 1. The complement of the union of two sets is equal to t...")
04:07, 24 May 2025 Thakshashila talk contribs created page Distributive Law of Sets (Created page with "= Distributive Law of Sets - Definition, Explanation, and Examples = The '''distributive law''' shows how union and intersection operations distribute over each other. It is a key property in set theory that helps simplify expressions involving both operations. == Distributive Law of Intersection over Union == For any three sets <math>A</math>, <math>B</math>, and <math>C</math>: <math> A \cap (B \cup C) = (A \cap B) \cup (A \cap C) </math> This means the intersecti...")
03:55, 24 May 2025 Thakshashila talk contribs created page Associative Law of Sets (Created page with "= Associative Law of Sets - Definition, Explanation, and Examples = The '''associative law''' is a fundamental property of set operations which states that when performing the same operation multiple times, the grouping (or association) of sets does not affect the result. == Associative Law for Union == For any three sets <math>A</math>, <math>B</math>, and <math>C</math>: <math> (A \cup B) \cup C = A \cup (B \cup C) </math> This means that whether you first unite <...")
03:47, 24 May 2025 Thakshashila talk contribs created page Commutative law on sets (Created page with "= Commutative Law of Sets - Definition, Explanation, and Examples = The '''commutative law''' is an important property of some set operations, meaning the order in which we perform the operation does not affect the result. == Commutative Law for Union == For any two sets <math>A</math> and <math>B</math>, the union operation is commutative. This means: <math> A \cup B = B \cup A </math> In words, combining set <math>A</math> with set <math>B</math> is the same as co...")
03:46, 24 May 2025 Thakshashila talk contribs created page Complement of a Set (Created page with "= Complement of a Set - Definition, Explanation, and Examples = The '''complement''' of a set contains all elements that are not in the set but belong to a larger, universal set. It helps identify what is "outside" a given set within a specified context. == Definition of Complement == Let <math>U</math> be the universal set, which contains all elements under consideration. The complement of a set <math>A</math>, denoted by <math>A'</math> or <math>\overline{A}</math>,...")
03:45, 24 May 2025 Thakshashila talk contribs created page Difference of Sets (Created page with "= Difference of Sets - Definition, Explanation, and Examples = The '''difference''' of two sets is an operation that finds elements that belong to one set but not the other. It is also called the '''relative complement'''. == Definition of Difference == The difference of sets <math>A</math> and <math>B</math>, denoted by <math>A - B</math>, is the set of all elements that are in <math>A</math> but not in <math>B</math>. Mathematically: <math>A - B = \{ x : x \in A \...")
03:44, 24 May 2025 Thakshashila talk contribs created page Intersection of Sets (Created page with "= Intersection of Sets - Definition, Explanation, and Examples = The '''intersection''' of two sets is an important set operation that finds all elements common to both sets. == Definition of Intersection == The intersection of two sets <math>A</math> and <math>B</math> is the set containing all elements that are in both <math>A</math> and <math>B</math>. It is denoted by: <math>A \cap B</math> Mathematically: <math>A \cap B = \{ x : x \in A \text{ and } x \in B \}...")
03:43, 24 May 2025 Thakshashila talk contribs created page Union of Sets (Created page with "= Union of Sets - Definition, Explanation, and Examples = The '''union''' of two sets is a fundamental operation in set theory. It combines all the elements from both sets into one set without repeating any element. == Definition of Union == The union of two sets <math>A</math> and <math>B</math> is the set containing all elements that belong to either <math>A</math>, or <math>B</math>, or both. It is denoted by: <math>A \cup B</math> Mathematically: <math>A \cup B...")
03:42, 24 May 2025 Thakshashila talk contribs created page Operations on sets (Created page with "= Operations on Sets - Overview and Basic Definitions = '''Operations on sets''' are procedures that combine or modify sets to form new sets. They are fundamental in set theory and are widely used in mathematics, computer science, and logic. == Basic Set Operations == Here are the most common operations on sets with brief explanations: * '''Union (∪)''': The union of two sets <math>A</math> and <math>B</math> is the set of all elements that are in <math>A</math> or...")
03:40, 24 May 2025 Thakshashila talk contribs created page Universal set (Created page with "= Universal Set - Definition and Examples = In set theory, the '''universal set''' is the set that contains '''all possible elements''' under consideration for a particular discussion or problem. It serves as the '''reference set''' or '''universe''' of discourse. == Definition of Universal Set == The '''universal set''' is usually denoted by <math>U</math>. It contains every element relevant to the context or subject being studied. For example, if we are discussing...")
03:38, 24 May 2025 Thakshashila talk contribs created page Proper subset (Created page with "= Proper Subset - Definition and Examples = A '''proper subset''' is a special kind of subset where all elements of one set are contained in another set, but the two sets are not equal. In other words, the proper subset must have fewer elements than the original set. == Definition of Proper Subset == A set <math>A</math> is called a '''proper subset''' of a set <math>B</math> if: * Every element of <math>A</math> is in <math>B</math>, and * <math>A</math> is not equa...")
03:37, 24 May 2025 Thakshashila talk contribs created page Subsets (Created page with "= Subsets - Definition, Types, and Examples = In set theory, a '''subset''' is a set whose elements all belong to another set. Subsets are fundamental in understanding the relationships between sets. == Definition of Subset == A set <math>A</math> is called a '''subset''' of a set <math>B</math> if every element of <math>A</math> is also an element of <math>B</math>. This is written as: <math>A \subseteq B</math> This means: <math>\forall x (x \in A \Rightarrow x \i...")
03:34, 24 May 2025 Thakshashila talk contribs created page Equal Sets (Created page with "= Equal Sets - Definition and Examples= In set theory, '''equal sets''' are sets that contain the '''exact same elements'''. The order of elements or how they are written does not matter, only the content does. == Definition of Equal Sets == Two sets A and B are said to be '''equal''' if they have '''exactly the same elements'''. This means every element of set A is in set B, and every element of set B is in set A. * Mathematically: <math>A = B \iff (x \in A \Rightar...")
03:34, 24 May 2025 Thakshashila talk contribs created page Singleton Set (Created page with "= Singleton Set - Definition and Examples = A '''singleton set''' is a special type of set that contains '''only one element'''. It is the smallest possible non-empty set in set theory. == Definition of a Singleton Set == A set that has '''exactly one element''' is called a '''singleton set'''. It is also known as a '''unit set'''. * In mathematical notation: <math>A = \{a\}</math> is a singleton set, because it contains only one element, '''a'''. == Characteristics...")
03:33, 24 May 2025 Thakshashila talk contribs created page Empty Set (Created page with "= Empty Set (Null Set) - Definition and Examples = The '''empty set''', also known as the '''null set''', is one of the most basic and important concepts in set theory. It refers to a set that '''contains no elements'''. It is often the starting point for understanding how sets behave. == Definition of Empty Set == An '''empty set''' is a set that has '''no elements''' in it. It is represented by: * <math>\emptyset</math> (the Greek letter phi) * or <math>\{\}</math...")
03:30, 24 May 2025 Thakshashila talk contribs created page Infinite Set (Created page with "= Infinite Set - Definition, Examples and Comparison = An '''infinite set''' is a set that contains an '''unlimited or uncountable number of elements'''. Unlike finite sets, infinite sets cannot be completely listed because they go on forever. == Definition of an Infinite Set == A set is called an '''infinite set''' if the number of its elements is '''not countable'''. In other words, it is impossible to list all the elements of the set completely, as they continue i...")
03:29, 24 May 2025 Thakshashila talk contribs created page Finite Set (Created page with "= Finite Set - Definition, Examples and Properties = A '''finite set''' is a type of set in mathematics that contains a '''countable number of distinct elements'''. This means the number of elements in the set is '''limited''' or '''fixed'''. Set theory often begins with understanding the concept of finite and infinite sets. == Definition of a Finite Set == A set is called a '''finite set''' if the number of elements in the set is '''countable''' and the process of li...")