Key Statistical and Machine Learning Concepts in Data Science

Posted on Dec 22, 2024 in Mathematics

Probability Distribution

Probability distribution gives the possibility of each outcome of a random experiment or event. It provides the probabilities of different possible occurrences. Probability distribution yields the possible outcomes for any random event. It is also defined based on the underlying sample space as a set of possible outcomes of any random experiment. These settings could be a set of real numbers, a set of vectors, or a set of any entities. It is a part of probability and statistics.

  • Cumulative Probability Distribution: The cumulative probability distribution is also known as a continuous probability distribution. In this distribution, the set of possible outcomes can take on values in a continuous range.
  • Discrete Probability Distribution: A distribution is called a discrete probability distribution where the set of outcomes are discrete.

Best Practices for Big Data

  1. Focusing on Specific Objectives: Having well-defined objectives provides a clear sense of purpose and direction for data analysis projects.
  2. Selecting High-Quality Data: The accuracy and reliability of data directly impact the quality of insights and decisions derived from analytics.
  3. Utilizing Pivot Tables: Pivot tables are powerful tools that enable the summarization and visualization of complex datasets, making it easier to draw insights and identify trends.
  4. Data Profiling: Data profiling serves as the foundation for understanding the quality, structure, and characteristics of the data.

Role of Analytical Tools in Big Data

Analytical tools play a crucial role in big data by enabling the processing, analysis, and visualization of large datasets. This allows businesses to extract meaningful insights, identify patterns, and make data-driven decisions by uncovering hidden correlations and trends within the vast amount of information collected, essentially transforming raw data into actionable intelligence.

Statistical Concepts in Big Data

  1. Descriptive Statistics: Understanding data through measures like mean, median, mode, standard deviation, and variance.
  2. Inferential Statistics: Drawing conclusions about a population based on a sample, using techniques like hypothesis testing and confidence intervals.
  3. Probability Theory: Quantifying uncertainty and randomness, essential for modeling and decision-making.
  4. Machine Learning: Employing algorithms to learn patterns from data, including regression, classification, and clustering.

Propositional Rule Learning

Propositional rule learning is a machine learning technique that aims to discover patterns in data by creating logical rules. These rules are expressed using propositions, which are statements that can be either true or false. Think of them as if-then statements, where the “if” part is a combination of propositions, and the “then” part is a single proposition. The data to be learned from is represented as a set of examples, where each example is described by a set of attributes (features) and a corresponding class label. For instance, if you’re predicting whether someone will buy a product, your attributes might be age, income, and location, with the class label being “buy” or “don’t buy.”

Regression Modeling

  1. Prepare Your Data: Clean, engineer, and split data.
  2. Choose a Model: Select a suitable regression model based on your problem.
  3. Train Your Model: Fit the model to your training data.
  4. Evaluate Your Model: Assess performance using appropriate metrics.
  5. Deploy Your Model: Integrate the model into a production environment.

Sampling and Resampling

Sampling

  1. The probability distribution of a statistic obtained from a large number of samples drawn from a specific population.
  2. It helps us understand the variability of a statistic and make inferences about the population parameter.

Resampling

  1. A statistical technique that involves drawing repeated samples from a dataset to estimate a population parameter or assess the variability of a statistic.
  2. It helps us estimate the uncertainty in statistical estimates and model performance.

Resampling

Resampling techniques, particularly bootstrapping, are often used to estimate the sampling distribution of a statistic. By repeatedly sampling from the original data, we can generate a large number of resamples, each with its own statistic. The distribution of these statistics approximates the sampling distribution of the original statistic.

Neural Networks

  1. Complex Pattern Recognition: Neural networks excel at identifying intricate patterns in large and complex datasets, making them ideal for tasks like image and speech recognition.
  2. Nonlinear Relationships: They can model complex, nonlinear relationships between variables, which traditional statistical methods often struggle with.
  3. Feature Learning: Neural networks can automatically learn relevant features from raw data, reducing the need for manual feature engineering.

Envision the Flow of Dynamics

  1. Visual Representation: Use flowcharts, diagrams, and mind maps.
  2. Simulation and Modeling: Employ system dynamics, agent-based, and CFD modeling.
  3. Data Visualization: Utilize time series plots, scatter plots, and heatmaps.
  4. Mathematical Modeling: Leverage differential equations and statistical models.

Clustering Strategies

  1. Partitioning Clustering: It is a type of clustering that divides the data into non-hierarchical groups. It is also known as the centroid-based method. The most common example of partitioning clustering is the K-Means clustering algorithm.
  2. Density-Based Clustering: The density-based clustering method connects the highly-dense areas into clusters, and the arbitrarily shaped distributions are formed as long as the dense region can be connected.
  3. Hierarchical Clustering: Hierarchical clustering can be used as an alternative for the partitioned clustering as there is no requirement of pre-specifying the number of clusters to be created. In this technique, the dataset is divided into clusters to create a tree-like structure, which is also called a dendrogram. The observations or any number of clusters can be selected by cutting the tree at the correct level. The most common example of this method is the Agglomerative Hierarchical algorithm.

Naïve Bayes Classifier

  1. The Naïve Bayes algorithm is a supervised learning algorithm, which is based on the Bayes theorem and used for solving classification problems.
  2. It is mainly used in text classification that includes a high-dimensional training dataset.
  3. The Naïve Bayes Classifier is one of the simple and most effective classification algorithms which helps in building the fast machine learning models that can make quick predictions.
  4. It is a probabilistic classifier, which means it predicts on the basis of the probability of an object.

Logistic Regression

Logistic regression is used for binary classification where we use a sigmoid function that takes input as independent variables and produces a probability value between 0 and 1. For example, we have two classes, Class 0 and Class 1. If the value of the logistic function for an input is greater than 0.5 (threshold value), then it belongs to Class 1; otherwise, it belongs to Class 0. It’s referred to as regression because it is the extension of linear regression but is mainly used for classification problems.

Decay Window

A decay window is a technique used in big data analytics to assign decreasing weights to older data points over time. This approach is essential for handling time-sensitive data streams where recent data is more relevant than historical data. As new data points arrive, they are assigned a higher weight. Older data points gradually lose their weight, often exponentially. This weighted approach ensures that recent data has a greater impact on calculations and analyses.

Real-Time Sentiment Analysis

Real-time Sentiment Analysis is a machine learning (ML) technique that automatically recognizes and extracts the sentiment in a text whenever it occurs. It is most commonly used to analyze brand and product mentions in live social comments and posts. An important thing to note is that real-time sentiment analysis can be done only from social media platforms that share live feeds, like Twitter does.

Permutation Test

A permutation test (also called a re-randomization test or shuffle test) is an exact statistical hypothesis test making use of the proof by contradiction. A permutation test involves two or more samples. The null hypothesis is that all samples come from the same distribution. Under the null hypothesis, the distribution of the test statistic is obtained by calculating all possible values of the test statistic under possible rearrangements of the observed data. Permutation tests are, therefore, a form of resampling. Permutation tests can be understood as surrogate data testing where the surrogate data under the null hypothesis are obtained through permutations of the original data.

Association Rule Mining

Association Rule Mining is a method for identifying frequent patterns, correlations, associations, or causal structures in datasets found in numerous databases such as relational databases, transactional databases, and other types of data repositories. The goal of association rule mining is to find the rules that allow us to predict the occurrence of a specific item based on the occurrences of the other items in the transaction.

  1. Market-Basket Analysis: In most supermarkets, data is collected using barcode scanners. This database is called the “market basket” database.
  2. Medical Diagnosis: Association rules in medical diagnosis can help physicians diagnose and treat patients.
  3. Census Data: The concept of Association Rule Mining is also used in dealing with the massive amount of census data.

Active Learning

A subset of machine learning known as “active learning” allows a learning algorithm to interactively query a user to label data with the desired outputs. The algorithm actively chooses from the pool of unlabeled data the subset of examples to be labeled next in active learning. The basic idea behind the active learner algorithm concept is that if an ML algorithm could select the data it wants to learn from, it might be able to achieve a higher degree of accuracy with fewer training labels.

Types of Hypothesis

  1. Simple Hypothesis: A Simple Hypothesis guesses a connection between two things. It says that there is a connection or difference between variables, but it doesn’t tell us which way the relationship goes.
  2. Complex Hypothesis: A Complex Hypothesis tells us what will happen when more than two things are connected. It looks at how different things interact and may be linked together.
  3. Directional Hypothesis: A Directional Hypothesis says how one thing is related to another. For example, it guesses that one thing will help or hurt another thing.

Compute Node Failure

  1. Redundancy and Fault Tolerance: Replicate data, use redundant hardware, and employ cluster management tools.
  2. Robust Job Scheduling and Monitoring: Utilize intelligent schedulers and monitoring tools to distribute and track jobs.
  3. Efficient Error Handling and Recovery: Implement retry mechanisms, checkpointing, and alerting systems.
  4. Scalability and Elasticity: Employ auto-scaling and horizontal scaling to adapt to workload changes.
  5. Regular Maintenance and Disaster Recovery: Perform regular maintenance, update software, and have robust backup and recovery plans.

Choosing Analytical Systems Over Conventional Systems

  1. Enhanced Decision-Making: Analytical systems provide deeper insights and predictive capabilities, enabling data-driven decisions.
  2. Scalability and Performance: Designed to handle massive datasets and complex queries, analytical systems offer superior performance and scalability.
  3. Advanced Analytics: Support for advanced techniques like machine learning, AI, and data mining, unlocking valuable insights.
  4. Cost-Effective: Optimized for data processing and storage, reducing operational costs and increasing efficiency.

Creating Analytics Through Active Learning

  1. Initial Data Labeling: Label a small, representative sample of data and train an initial model.
  2. Active Learning Loop: Iteratively select informative unlabeled data, label them, retrain the model, and repeat.
  3. Model Evaluation: Evaluate the model’s performance using appropriate metrics and analyze errors.
  4. Deployment and Monitoring: Deploy the model, monitor its performance, and retrain as needed.

Randomization Test

In a randomization test, the distribution of test statistics is computed over all possible permutations of the treatment labels. The treatment assignments are presumed to be done at random so that all assignments are equally likely. To evaluate the hypothesis of no treatment effect using the randomization test, one needs to carry out the following:

  1. Compute a relevant test statistic for collected data. The statistic is chosen so that it could differentiate between the null and the alternative.
  2. Enumerate all possible treatment assignments and compute the statistic for each permutation to construct the randomization distribution of the test statistic under the null.
  3. Compute the p-value of the test statistic using the randomization distribution.

DF Multistage and Multihash

Multistage

  1. Multiple Passes: Involves multiple passes over the dataset, each pass using a different hash function.
  2. Reduced Candidate Set: Each pass reduces the number of candidate itemsets, improving efficiency.
  3. Increased Memory Usage: Requires more memory as it maintains multiple hash tables.

Multihash

  1. Single Pass: Uses multiple hash functions in a single pass over the dataset.
  2. Reduced Memory Usage: Requires less memory compared to multistage, as it uses fewer hash tables.
  3. Potential for Overcounting: While efficient, it might overcount some itemsets, leading to a less accurate result.

Stream Query

A stream query operates on one or two streams to transform their contents into a single output stream. A stream query definition declares an identifier for the items in the stream so that the item can be referred to by the operators in the stream query. When the correlator executes a statement that contains a stream query definition, the correlator creates a new stream query. Each stream query has an output stream.

Monotonicity

A Monotonicity relationship occurs when an input value is increased and the output value either only increases (positively constrained) or only decreases (negatively constrained), and vice versa. For example, if the ratio of payment to balance owed on a loan or credit card increases, we would expect that the credit risk score should improve (lower risk of default). Figure 1 shows a positively constrained monotonic relationship between these two variables.

Repeated Measures Analysis

Repeated measures data comes from experiments where you take observations repeatedly over time. Under a repeated measures experiment, experimental units are observed at multiple points in time. So instead of looking at an observation at one point in time, we will look at data from more than one point in time. With this type of data, we are looking at only a single response variable but measured over time.