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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 ...
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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) ...
user14261785's user avatar
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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 ...
user avatar
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 ...
user23358153's user avatar
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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 ...
Martin's user avatar
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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 ...
Sherlock_Hound's user avatar
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, ...
Luis's user avatar
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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 ...
elemolotiv's user avatar
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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 ...
Yandle's user avatar
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4 votes
1 answer
411 views

Why does the Monte Carlo estimate not depend on the dimension

The Monte Carlo Estimator for some event probability (e.g., for the "failure probability") is defined as follows: $$ \hat\mu = 1/N \sum_{i=1}^N I(\boldsymbol{x}_i), $$ where $\boldsymbol{x}...
David Braun's user avatar
1 vote
0 answers
36 views

Dimensions of posterior and likelihood in bayes theorem

I'm trying to do an instrument calibration, and I'm following a source which I don't quite understand. I can set $j$, which takes values 0-63, and measure $\vec{Q}$, which is a four element vector ...
Wyatt's user avatar
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4 votes
3 answers
321 views

Curse of dimensionality: How PCA improves my model?

After having read about the curse of dimensionality, I have been looking into a filtered version of the Superconductivity dataset. The number of dimensions is 81, so initially I thought that reducing ...
Alfonso_MA's user avatar
0 votes
1 answer
188 views

Predicting continuous variable from 3d coordinates

I have a dataset containing independent variables as three different 3-D coordinates. For reference, the data is structured like this Independent 1: (1,2,3) , (4,5,6)... Independent 2: (7,8,9), (10,11,...
power_of_epi's user avatar
2 votes
1 answer
469 views

Why curse of dimensionality affects more non-parametric approaches?

I just want to know the reason why the curse of dimensionality mostly affects the non-parametric approaches compared with parametric ones.
olad uhg's user avatar
1 vote
1 answer
690 views

How to check whether two image datasets come from the same distribution? [duplicate]

In the literature of transfer learning and domain adaptation everyone talks about two datasets having different feature spaces and different distributions. In case of having image datasets, I think I ...
samsambakster's user avatar
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0 answers
86 views

Measure for how much a data deviates from "perfectly symmetric/ideally distributed" in data's units?

Measure for how much a data deviates from "perfectly symmetric/ideally distributed" in data's units? How do I produce a skewness/asymmetry/something measure that's in the same units as the ...
mavavilj's user avatar
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1 vote
0 answers
113 views

How does t-SNE preserves embedding orders?

According to the triplet loss Wikipedia page: t-SNE (t-distributed Stochastic Neighbor Embedding) preserves embedding orders via probability distributions, whereas triplet loss works directly on ...
Revolucion for Monica's user avatar
3 votes
1 answer
181 views

Wilks' theorem when dimension of submodel is not well defined

Suppose $\{f(\cdot,\theta) : \theta \in \mathbb{R}^p\}$ is a statistical model satisfying the conditions for Wilks' theorem, and that we have a hypothesis test of the form: $$H_0: \theta_p >0$$ $$...
yasinibrahim30's user avatar
0 votes
1 answer
296 views

Can machine learning be used with data where each dimension is different?

Let's suppose that I have some data, and I have a vector representation of each data point. For example, one data point might look like this: [0, 1, 0, 3, -2, 2.3]. Now suppose that for each vector, ...
JBraha's user avatar
  • 103
2 votes
2 answers
1k views

Matrix and vectors, why different notation for dimensions?

If we collect data and put it into a matrix of size (100,3), we tend to say we have three-dimensional data. We think of each column as a dimension. On the other side, if we have a vector of size (100,...
Stenga's user avatar
  • 251
3 votes
1 answer
909 views

Why aren't the coskewness and cokurtosis matrices square like the covariance matrix?

The variance-covariance matrix is shaped $p\times p$, whereas the co-skewness matrix is shaped $p\times p^2$ and the co-kurtosis matrix is $p\times p^3$. Why is this, given that skewness and kurtosis ...
develarist's user avatar
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2 votes
1 answer
120 views

What is a unit $n$-cube, and its connection to the support of a distribution?

In statistics, what is an intuitive way of saying what an $n$-cube is? how do support of distributions come to be defined by an $n$-cube? are $n$-cubes useful in any applications beyond being a ...
develarist's user avatar
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1 vote
1 answer
71 views

Doubts on how to write in vector

I know I can write a vector like this: $\beta = ( \beta_{1}, \dots, \beta_{p})^{\top}$ and $\rho = (\rho_{1}, \dots, \rho_{q})^{\top}$ by this way it have dimension $p \times 1$ and $q \times 1$, ...
Bruno's user avatar
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0 votes
1 answer
160 views

How can a covariance matrix for a normal distribution not be quadratic?

Currently Im reading this paper and in section 3.3., I came across the definition of a multi-dimensional standard normal distribution: \begin{align} q(\pmb{\epsilon}) = \mathcal{N}(\textbf{0}, \...
MJimitater's user avatar
1 vote
1 answer
83 views

How do the units of the SIR model cancel out?

I was having trouble trying to understand the parameters of the simplest SIR model. If beta is the effective contact rate and s is the percentage of people who are susceptible, then how do the units ...
Krishna Kalakkad's user avatar
0 votes
1 answer
32 views

M -> N regression where N > M

I am seeking to perform a realtime mapping of M input features to N output parameters where N > M, e.g 2 inputs to 10 outputs. In my use-case I would define ...
j b's user avatar
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0 votes
0 answers
39 views

Dimensions in Kmeans cluster plot [duplicate]

I did a kmeans cluster plot to identify how my plants cluster based on 4 morphological traits of them. It gave me 3 clusters as shown in the figure. I'm not sure how to interpret these dimensions ...
Hans's user avatar
  • 1
1 vote
0 answers
92 views

Checking if my categorical variables are really unidimensional, ordinal

I have 6 categorical variables that can have the values -1, 0 and +1. The extremes are assigned to a semantic label. During rating, the rater could select either one of the labels (-1, +1) or neither ...
ruhig brauner's user avatar
1 vote
0 answers
30 views

Change of variables: 4-dimensional PDF to 2-dimensional PDF

I have a 4-dimensional joint-PDF between variables $X_1,X_2,X_3,X_4$ which are all Gaussian. I want to transform this into a 2-dimensional joint-PDF between new variables $Y_1=Y_1(X_1,X_2,X_3,X_4)$ ...
zack's user avatar
  • 143
0 votes
1 answer
58 views

Question regarding machine learning models in production

for example, i have a feature with 5 distinct values and once one hot encoded this becomes 5 columns, but lets say the data that needs to be predicted has 4 distinct values, the neural network won't ...
A.H.'s user avatar
  • 1
0 votes
1 answer
120 views

Determine which dimensions are good predictors for regression

I have a n-dimensional data that maps to a 1D value. I want to train a regressor, so given a new sample I can predict the outcome. The problem is that I don't know which of this n-dimensions are ...
Elerium115's user avatar
4 votes
2 answers
246 views

Calculating multivariate integrals between lower and upper bounds

Suppose $\vec{X}=(x_1,x_2,...,x_n)$ follows some continuous multivariate distribution, such that $x_i\in{\rm I\!R}, i=1,...,n$. Suppose also that I have access to the following functions: $\phi(\...
Felipe D.'s user avatar
  • 268
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. ...
Emna Jaoua's user avatar
-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 ...
andrewH's user avatar
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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 ...
andrewH's user avatar
  • 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 ...
Diogo Santos's user avatar
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 ...
whatamess's user avatar
  • 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 ...
mzmyslowski's user avatar
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 ...
Hyunjun Kim's user avatar
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 ...
Leen's user avatar
  • 21
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 ...
sereizam's user avatar
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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 ...
user avatar
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 ...
Lay González's user avatar
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 ...
Jane Wayne's user avatar
  • 1,399
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 ...
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