Covariance

Covariance is one of a family of statistical measures used to analyze the linear relationship between two variables.

How do two variables behave as PAIR?

There are certain terminology like covariance, correlation, linear regression etc.. make confuse how all are related to each other. here linear regression related to correlation which is related to covariance in nature so all this measures analyses by looking with linear relationship between two variables.

Covariance is a Descriptive measure of the linear association between two variables that is very simple to interpret.

1. A positive value indicates a direct or increasing linear relationship.

2. A negative value indicates a decreasing relationship.

A concept here is the direction that is sign on the covariance whether it is positive or negative

For Example, if we have 4 quadrants like (I ,II ,III ,IV)

I - (+,+) : represents the both x and y values are positive.

II - (-,+) : represents the x is negative and y is positive.

III - (-,-) : represents the both x and y values are negative.

IV - (+,-) : represents the x is positive and y is negative.

In I and III quadrant variables move in same direction that is called covariance positive means if x goes up than y goes up. In quadrant I, x goes down than y goes down in quadrant III so slop in this quadrant is positive.

lets take another direction for II and IV, In this case if x goes down but y increases in II so that variables are exhibiting opposite behavior or x goes up but y decreases in IV so if variables move in opposite direction in this case it is negative covariance because slop is negative.

In some case, All points are mixed up in all quadrant so here variables are seems to have no linear relationship In this case the covariance is near or equal to zero.

Comments

Post a Comment

Popular posts from this blog

Transformers: Self-attention

Image
 In the realm of neural networks, three primary types are commonly discussed: Artificial Neural Networks (ANNs) : These are fully connected networks comprising input, hidden, and output layers. Each neuron in a layer is connected to every neuron in the subsequent layer, enabling complex pattern recognition through weighted connections. Convolutional Neural Networks (CNNs) : CNNs incorporate convolutional layers with kernels (filters) that slide across the input data to detect features. These networks also perform pooling operations to reduce dimensionality and flatten the data before passing it to fully connected layers. CNNs are particularly effective for image and spatial data processing. Recurrent Neural Networks (RNNs) : RNNs are designed to handle sequential data by maintaining a memory of previous inputs through their hidden states. Unlike feed-forward networks, RNNs can process input sequences of variable length, making them suitable for tasks involving time series data, nat...
Read more

Retrieval Augmented Generation(RAG)

Image
 We Know core ideas like NLP, LLM. Let's look at how we might build utilizing LLM and the deployment aspect using RAG. Retrieval-Augmented Generation (RAG) is a technique in natural language processing that combines retrieval-based and generation-based approaches to create more accurate and informative responses. Let's break down each point: 1. RAG Architecture  Architecture: Retriever: Retrieves relevant documents or passages from a large corpus based on the input query. Reader/Generator: Uses the retrieved documents to generate a coherent and relevant response. Combiner: Integrates the retrieved information with the generated response. 2. Pipeline Behind the RAG The RAG pipeline is a collection of the above components working together: Query Processing: The input query is encoded into a vector. Retrieval: The encoded query is used to retrieve relevant documents from a vector database. Document Encoding: The retrieved documents are encoded into vectors. Information Inte...
Read more

Large Language Models(LLMs)

Image
  Language Model A language model is a type of artificial intelligence model designed to understand, generate, and manipulate human language. Language models are trained on large datasets of text to learn patterns in language use, including grammar, vocabulary, and context. Key functions include: Text Generation : Producing coherent and contextually relevant text. Text Completion : Predicting the next word or phrase in a given context. Machine Translation : Translating text from one language to another. Sentiment Analysis : Determining the sentiment expressed in a piece of text. Text Summarization : Creating concise summaries of longer texts. Language models can be based on various architectures, such as Recurrent Neural Networks (RNNs) and Transformer models. Large Language Model (LLM) A large language model (LLM) is a type of language model that is characterized by its large size, typically measured by the number of parameters (weights) it has. LLMs are trained on vast amounts ...
Read more