# Questions tagged [linear-algebra]

A field of mathematics concerned with the study of finite dimensional vector spaces, including matrices and their manipulation, which are important in statistics.

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### Hypothesis vs Hyperplane in Machine Learning

I am finding it hard to understand the clear difference between Hypothesis and Hyperplane. I know that Hypothesis is a candidate model that maps inputs to outputs after training. And, Hyperplane is ...
71 views
+50

### What type of technique can be used to solve this question?

Apology for the ambiguous title, I do not know the term. I have data of some products which a few variables: origin, weight, brand. For example: Product A = "China, 100g, Brand X" Product ...
120 views

### How to incorporate the uncertainty of the model coefficients in the prediction interval of a multiple linear regression

I'm dealing with modeling small experimental data sets. As most experimental work does not generate thousands of samples, but rather a handful, I need to be inventive about how to deal with this small ...
79 views

### Can I use regression to solve a multiple equation problem

I'm working on a problem which is a multiple equation. I have a group of people and each person in the group is working on different tasks (e.g. n tasks in total). Each person in this group is working ...
59 views

1 vote
17 views

### Outlier detection with elliptic envelope - unexpected error

I am trying to detect outliers with sklearn.covariance.EllipticEnvelope for a single variable, but it throws an unexpected error. Here is an example the reproduces ...
1 vote
65 views

### Affine 2D mapping in python

I have two sets of 2D data $A$ and $B$ (representing 2D positions on a 2D plane $x,y$) which are related (the first pair of $x,y$ of $A$ is related to the first pair of $x,y$ of $B$ for instance). I ...
1 vote
964 views

### Linear regression with a fixed intercept and everything is in log

I have a set of values for a surface (in pixels) that becomes bigger over time (exponentially). The surface consists of cells that divide over time. After doing some modelling, I came up with the ...
151 views

### About the last decoder layer in transformer architecture

So, in the decoder layer of transfomer, suppose I have predicted 3 words till now, including the start token then the last decoder layer will produce 3 vectors of size d-model, and only the last ...
39 views

1 vote
125 views

### What are some application of Google's PageRank Algorithm in Data Science

I came across a topic on computational linear algebra that talks about iterative algorithms to compute eigenvalues. I've worked with power method which is an iterative algorithm that converges a ...
180 views

### Inverting a matrix using a convolutional neural network

Just for a fun exercise, I am trying to invert a matrix, say size 28x28 (or even 5x5) with a neural network. The way I approached this (quite naively) is as follows: I built a fully convolutional ...
68 views

### Why do we use 'T' when we are to say matrix-vector product? [closed]

On the first picture author uses $T$ meaning matrix-vector product But other website do not use $T$, but says that $x$ is a vector, I do not understand if it is important or not
4k views

### 3d input for Dense Layer Keras

Is there any example of how Keras Dense layer handles 3D input. The documentation explains the following: ...
88 views

### What is the Intuition behind weight vector W which is normal to the plane? Is the weight vector W same as the W which is normal to the plane π?

In an interview, I was asked the intuition behind the weight vector. I told the weight vector is a vector which we try to minimize to a local minima with the help of regulariser so we don't overfit. ...
1 vote
730 views

### How does the equation "dW = - (2 * (X^T ).dot(Y - Y_hat)) / m" comes in Linear Regression (using Matrix + Gradient Descent)?

I was trying to code the Linear Regression in Python using Matrix Multiplication method using Gradient Descent and followed a code where there was no mention what is the loss but just a code as Per ...
152 views

### Geometric classification models

In class we have been presented with a Geometric classification model such that the goal is to construct a linear decision boundary $\bf{w} \cdot \bf{x} = t$; where $\bf{w}$ is the vector from the ...
38 views

### How does tree-based algorithms handle linearly combined features?

While I am aware that tree-based algorithms (e.g., DT, RF, XGBoost) are 'immune' to multi-collinearity, how do they handle linearly combined features? For example, is there is any additional value or ...
66 views

### Intuition behind understanding eigenvectors and Machine Learning [closed]

I am struggling to understand linear algebra application in machine learning, and I am not able to answer the following question. Is the model learned in Machine Learning the eigenvector of the ...
1 vote
59 views

### How effective is Moore Penrose for solving regression problems with overdetermined system of equations?

For regression problems with #Predictors > #observations, I recently read about Moore Penrose (pseudo inverse method) which solves the problem of non invertible matrix in OLS for regression problems. ...
245 views

### Best linear algebra library for C++?

I have been trying to find the substitute of numpy and perform some linear algebra using C++. Here's a list of the libraries I have encountered: Eigen Armadillo Dlib GNU Scientific library Please ...