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# Questions tagged [dimensions]

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### How can I augment a 1D tablar dataset using an additional 2D dataset?

I have the following two types of datasets: The dataset-1 is a tabular data that describe 7000 proteins. dataset-1 is only one file. dataset-2 consists of 7000 individual data files that are 2D ...
• 2,201
0 votes
0 answers
11 views

### What if there is only one measurement equation containing two (or more) state variables while there are two unobservable state variables in a model?

I am learning Kalman Filter and ran into a question about the case in which only one signal is available. It is commonly assumed that the number of states equals the number of observations (signals) ...
0 votes
0 answers
13 views

### R issue: lm() is printing NAs for rows once ncol > nrow [duplicate]

I'm running an lm() on lagged variables as part of a network analysis, and have the following dimensions: dim(final) [1] 197 277 dim(final_lag) [1] 197 831 The ...
1 vote
0 answers
42 views

### How to compute relative error of multi-dimensional time-series?

I have written a python script that uses a variety of different integrators to simulate the gravitational N-body problem. I would like to compare the positions obtained from my simulation to the ...
0 votes
0 answers
25 views

### How to handle a dependent variable with sub-dimensions and multiple independent variables with sub-dimensions?

The variables X1, X2 and Y consist of several dimensions (based on the corresponding literature), which we asked about in advance using Likert items (1-5). However, I am not quite sure how to analyze ...
0 votes
0 answers
17 views

### what does edge mean in the context of sample space?

This is a follow-up question on this post It uses a term 'edge'. For example, it says I understand that extrapolation is harder than interpolation. And I understand that if we choose a point to ...
0 votes
1 answer
155 views

### RNN weight and state matrices

Implementations of RNN in NLP tasks, like those in https://dennybritz.com/posts/wildml/recurrent-neural-networks-tutorial-part-2/, are done using matrices, that are used to store the inputs, outputs, ...
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1 vote
1 answer
73 views

### Measure the "actual" number of dimentions in a multivariate distribution

Consider a 3D multivariate normal distribution $x\sim N(0,\Sigma)$ where $$\Sigma=\begin{bmatrix}1 &1 &0 \\ 1&1&0 \\ 0 &0& 1 \end{bmatrix}$$ Since $x_1$ and $x_2$ are fully ...
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0 votes
0 answers
105 views

### Euclidean distance between points in high dimensions

On Wikipedia there's a statement: When a measure such as a Euclidean distance is defined using many coordinates, there is little difference in the distances between different pairs of samples. Is ...
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4 votes
1 answer
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1 vote
0 answers
408 views

### How can we know the encoding dimension in the autoencoder model?

I have a very basic autoencoder model. I am trying to train it on one hot encoded vector. ...
• 233
-1 votes
1 answer
134 views

### Dimensional analysis for a qdf/quantile function correspondng to the pdf/CDF (income distribution example)

This question is a duplicate of a question I previously asked, here: Dimensional analysis for a qdf/quantile function corresponing to the pdf/CDF (size distribution of income example). I believe I ...
• 3,157
1 vote
0 answers
106 views

### Dimensional analysis for a qdf/quantile function corresponing to the pdf/CDF (size distribution of income example) [duplicate]

I am going to frame this question in terms of a pdf and quantile functions for the size distribution of income, because that is where I have currently encountered it, but similar questions in quite ...
• 3,157
0 votes
0 answers
267 views

### Importance Sampling for n dimensions

EDIT: I edited the question in order to make it clear. I'm having a problem with Importance Sampling and calculation of weights in more than one dimension. Because for me this is not obvious, I will ...
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3 votes
1 answer
585 views

### Estimating dimensionality of feature space from distance matrix

I have a distance matrix with some noise (e.g. obtained by asking people how similar two objects from a set of objects are). I am interesting in finding the (best guess for the) dimensionality of the ...
• 151
2 votes
1 answer
1k views

### Can't update bias using gradient descent, because derivative of loss function with respect to bias has different dimensions

I want to update a bias in my Neural Network using the gradient descent optimization algorithm. Unfortunately, the bias has different dimensions than the derivative of the loss function with respect ...
1 vote
1 answer
31 views

### Definition of dimension [closed]

For example, there is a matrix A = [[1, 2, 3, 4], [5, 6, 7, 8]] where A is a 2 dimensional matrix with 2 samples of 4 dimensions. I guess word dimension ...
1 vote
1 answer
49 views

### How can I visualise and understand the relationship between n dimensions [closed]

I am new at the field of machine learning. I have non-linear 6 dimensions, and I want to understand the relationship between 5 dimensions first. And, then understand how these 5 dimensions behave ...
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46 votes
3 answers
98k views

### Understanding input_shape parameter in LSTM with Keras

I'm trying to use the example described in the Keras documentation named "Stacked LSTM for sequence classification" (see code below) and can't figure out the ...
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1 vote
1 answer
1k views

### Can a triangle plot be used for metrics that do not sum to 100%?

From wikipedia: A ternary plot, ternary graph, triangle plot, simplex plot, or de Finetti diagram is a barycentric plot on three variables which sum to a constant. However, I want to use the plot ...
4 votes
3 answers
3k views

### Why correlation is not "transitive"?

First let me explain what I mean by "transitive" Suppose that the price of product A and the price of product B has a correlation of .5 Suppose also that the price of product B and product C has a ...
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1 vote
2 answers
459 views

### The impact of the number of dimensions on classification/predictive performance

For the sake of simplicity, let's say we have a rectangular dataset where the columns are fields/variables and the rows are observations/events. According to the curse of dimensionality, the higher ...
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12 votes
4 answers
1k views

### Estimating the dimension of a data set

A colleague in applied statistics sent me this: "I was wondering if you know any way to find out the true dimension of the domain of a function. For example, a circle is a one dimensional ...