Questions tagged [intuition]

Questions that seek a conceptual or non-mathematical understanding of statistics.

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0answers
14 views

How do we visualize the Decomposition of Variance formula $\text{Var}[y] = \text{Var}_x[\text{E}[y|x]] + \text{E}_x[\text{Var}[y|x]]$?

The Decomposition of Variance formula is $\text{Var}[Y] = \text{Var}_X[\text{E}[Y|X]] + \text{E}_X[\text{Var}[Y|X]]$. This can be described as follows: the variance of y decomposes into the variance ...
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13 views

Why does the autocorrelation of a wide-sense stationary stochastic process only depend on lag? [closed]

$$\mathbf{E}\left[x(t_1)x(t_2)\right] = \mathbf{E}\left[x(t_1+\Delta t)x(t_2+\Delta t)\right] \neq \mathbf{E}\left[x(t_1)x(t_3)\right] $$ $$t_2 = t_1+\tau$$ I'm trying to picture how this is the case ...
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2answers
36 views

L2 regularization and its intuition

I am reading about L2 Regularization. As far as I know we add a thing to the loss function that: $$J(w) = LOSS + \lambda w^T w$$ In the book Deep Learning by Goodfellow et al., they stated "...
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19 views

How to develop intuition to reason about models/predictions

I am trying to answer a few questions that I was asked about data science and was wondering what the best way is (from your experience) to develop the qualitative/quantitative intuition behind ...
2
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0answers
40 views

What is the intuition of a dual?

I have been hearing that the Ridge regression is the dual to the GP (Gaussian process regression). What does this mean? Can someone please give an intuition on what 'dual' is. My impression of the '...
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0answers
26 views

Intuitive explanation of rules of do-calculus

Do-calculus has 3 rules: https://plato.stanford.edu/entries/causal-models/do-calculus.html I understand them on a mathematical level, but they seem so arbitrary. I can not wrap my head around what the ...
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0answers
22 views

Probability Density Function (PDF) Intuition [duplicate]

I know what is Probability Density Function and its application in Machine Learning and Statistics. The problem I faced is that how does it being calculated? For a specific example like the ...
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0answers
31 views

Intuitive way to connect gamma and chi-squared distributions

I understand that a chi-squared distribution is a special case of the gamma distribution. However, I find claims of "the math just works out" to be an unhelpful in remembering or ...
2
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1answer
18 views

Intuition for relationship between variance of geometric and exponential distributions

Given that the exponential distribution can be thought of as a continuous version of the geometric, is there an intuitive way to relate their variances? I have some intuition for how the means of ...
2
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0answers
35 views

Intuitive explanation of the paper “Generalized Random Forests” (Athey, Tibshirani, Wager)

This seems like an exciting approach to uplift modelling, but the only resource that I can find is this paper and it is too brief, notation-heavy and dense to be of any use to me. I have an honours ...
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1answer
34 views

Intuition behind clustering standard errors

Intuitively, why does a lack of clustering standard errors lead to erroneously smaller standard errors? Looking at the calculations and seeing the difference between SEs that are clustered and not ...
3
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1answer
100 views

Intuition behind projection matrix

I'm new to machine learning and came across projection matrix . In a random thread it was interpreted as The matrix $X(X^\text{T} X)^{-1} X^\text{T}$ is a projection matrix, as it does precisely that:...
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22 views

VAR($p$) estimation

I am bit stumped by this result. Source: Remark on page 46 of Multivariate Time Series Analysis by Rsay. ... one can obtain the GLS estimate of a VAR($p$) model equation by equation. That is, one can ...
2
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1answer
218 views

What is MCRMSE (mean columnwise root mean squared error)?

The MCRMSE evaluation metric was used in the Kaggle Competitions Africa Soil Property Prediction Challenge(6 years ago) and OpenVaccine: COVID-19 mRNA Vaccine Degradation Prediction(On-going) ...
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0answers
58 views

Are the following model assumptions on a data stream too restrictive?

Suppose that you were to model a "generic" continuous-time real-world data signal $X$ taking values in a bounded continuum $K\subset\mathbb{R}^d$ (e.g. the body temperature of a patient or ...
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0answers
22 views

Intuition on why Gibbs Sampling samples from the posterior distribution

I am new to Gibbs Sampling and I do understand how the algorithm works but I would also like to understand how sampling from the conditional distributions is equivalent to sampling from the joint. ...
11
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1answer
111 views

What does $P(|X_n - X| \geq \epsilon)$ represent intuitively?

I get that $P(|X_n - c| \geq \epsilon)$ represents the probability that the random variable $X_n$ is outside the interval of $(c - \epsilon, c + \epsilon)$ but I am not sure how it works with a random ...
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44 views

Can Principal Component Analysis Be Used Here?

My professor has given us test prep in the form of a scenario essay question (For studying purposes/not graded) I want to see if my method of Principal Component Analysis would be applicable here. I ...
9
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1answer
154 views

What's an intuitive way to understand how KL divergence differs from other similarity metrics?

The general intuition I have seen for KL divergence is that it computes the difference in expected length sampling from distribution $P$ with an optimal code for $P$ versus sampling from distribution $...
2
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1answer
34 views

Intuition behind replacing backpropagation with random matrices

In a recent paper on the experimental results of when neural networks learn via directed feedback alignment, https://arxiv.org/pdf/2006.12878.pdf, it was shown that directed feedback alignment ...
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2answers
248 views

Do we want to move away from significance?

Recently I have found that many statisticians are speaking of moving away from significance. I understand that many studies base their conclusions on p-values, which I agree can be misleading at ...
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1answer
83 views

Does using Cross-Validation give you the green light to do exhaustive hyper-parameter searches?

By hyper-parameters I mean not only the machine learning algorithm hyper-parameters (learning rate, etc.), but also hyper-parameters like "what's the ideal number of data points to use" or &...
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1answer
46 views

Do we update a priori distribution somehow?

I'm trying to understand Bayesian statistics. Recently I asked here whether we estimate paramteres of a priori distribution in bayesian statistics. I was responded that we typically don't estimate ...
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2answers
69 views

Statistics book recommendation for absolute beginners and non-mathematics people

Based on this this and this, but also looking for following specifications For absolute beginners level, and easy type book. Easy to read (Less text, larger fonts). Not mathematically rigorous. More ...
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0answers
26 views

What is a generalized linear model

Generalized linear models have become so central to effective statistical data analysis, however, that it is worth the additional effort required to acquire a basic understanding of the subject. I am ...
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0answers
23 views

maximum Corelation coefficient - how the numarator and denominator becomes equal?

Pearsons corelation coefficient is defined as follows $$ r_{x,y} =\frac {\sum (x_i -\bar X)(y_i - \bar Y)}{\sqrt{\sum(x_i-\bar X)^2} \sqrt{\sum(y_i-\bar Y)^2}} $$. Now, maximum magnitude of a ...
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2answers
58 views

Intuitive Explanation of “AutoEncoders”

To my knowledge, Autoencoders are an unsupervised learning technique in which we leverage neural networks for the task of representation learning. I know there is a lot of topics around autoencoders, ...
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0answers
9 views

Making sense of Max-margin loss

I'm a bit confused about what and how Max-margin loss is calculated. I'm looking for intuition in words but also some simple insight into mathematical calculations (I don't know if the latter is ...
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1answer
47 views

Intuitive explanation on “Generalization ” [closed]

I recently worked on Generalization of Gradients. If I'm asked to find Generalization of Gradients or for Dirichlet distribution, etc. I'll do it correctly like a machine. But I didn't understand it. ...
4
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1answer
49 views

Intuition behind m-out-of-n bootstrap

I am trying to get some intuition on why m-out-of-n bootstrap works but haven't been able to find good explanation. I would really appreciate any input on this. I think I do understand what bootstrap ...
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0answers
22 views

Properties of the diff of a sorted uniformly generated set

I am studying a set of uniformly generated points, more concretely the distance between the points. When the set is unsorted the histrogram shows it is normally distributed and that matches my ...
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8answers
2k views

Intuitive explanation of “Statistical Inference”

What is the cleanest, easiest way to explain someone the concept of Inference? What does it intuitively mean? How would you go to explain it to the layperson, or to a person who has studied a very ...
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0answers
25 views

What are the appropriate ways of performing model selection? [closed]

I am reading up on model selection and ran into some intresting questions that I would like to understand to build intuition on the topic. My questions were: What are the appropriate ways of ...
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1answer
46 views

Intuition behind the use of multiple attention heads

Consider this introduction to attention layers with the main description below. I understand attention layers as learnable soft query retrieval operators that act on a "K-V store" of vectors....
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1answer
45 views

How to Compare Variances?

I have a dataset which contains height and weight variables. The mean and variance for height are 165 cm and 25 cm. The mean and variance for weight are 70 kg and 16 kg. How to compare variances of ...
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0answers
12 views

Beta distribution meaning? [duplicate]

I am trying to understand what is the meaning of Beta distribution. I can try compare it to classical probability of event that when I throw the dice it will be let's say 1, that is 1/6. Btw also try ...
39
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6answers
3k views

Debunking wrong CLT statement

The central limit theorem (CLT) gives some nice properties about converging to a normal distribution. Prior to studying statistics formally, I was under the extremely wrong impression that the CLT ...
0
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1answer
37 views

Intuition behind spectral density of time series

Is there any intuition behind the spectral density $f(\lambda)$ of a time series, where $$ f(\lambda)= \frac{1}{2\pi}\sum_{h=-\infty}^{+\infty}{e^{-ih\lambda}\gamma(h)}, -\infty < \lambda < \...
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0answers
45 views

How to explain a Box Plot?

Assuming that I'm able to augment their knowledge about boxplot I can give the below insights for box plot ...
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3answers
291 views

Permutation tests and exchangeability [duplicate]

Permutation tests assume exchangeability of the response/observations under the null hypothesis. In what practical situations is this clearly violated? When is it unproblematic? Edit/additional ...
2
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1answer
86 views

Intuitive explanation of “invariance”

...assuming that I'm able to augment their knowledge about variance in an intuitive fashion Understanding "variance" intuitively and about covariance How would you explain covariance to ...
4
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3answers
114 views

Foundations behind Linear Regression / Statistical Modelling

I've always struggled with the foundations behind the concept of modelling (and specifically regression) - what is random, what is not, what we are modelling. I think I have a grasp of it - but I'd ...
36
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4answers
2k views

Intuitive explanation of Kolmogorov Smirnov Test

What is the cleanest, easiest way to explain someone the concept of Kolmogorov Smirnov Test? What does it intuitively mean? It's a concept that I have difficulty in articulating - especially when ...
0
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1answer
49 views

Interpretation for changes in a $\chi^2$'s density as $k$ increases

The chi-square's density becomes more regular as $k$ increases: $k=1$ unbounded, convex $k=2$ bounded, convex $k=3$ close to 0 near 0, unbounded positive slope $k=4$ close to 0 near 0, bounded ...
2
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2answers
68 views

What is an intuitive way for choosing the right Statistical test?

In my Statistics class, we just talked about Statistical tests. So far I’ve been understanding the material, okay, but now I’m very confused. I get that Statistical tests are used in hypothesis ...
20
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5answers
2k views

Can someone explain the importance of mean stationarity in time series?

In regular regression, the expected value of Y | X is allowed to change. In fact we generally use regression when we want to model this change in conditional mean. I am not understanding why in time ...
6
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2answers
114 views

Intuition for why the (log) partition function matters?

I'm on a quest for the intuition behind the fact that theoretical introductions to approximate inference focus so much on the log partition function. Say we have a regular exponential family $$p(\...
2
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2answers
115 views

Central limit theorem seems counterintuitive given Law of large number

From what I understand, the Central limit theorem says the sample mean is distributed normally when sample number tends to infinity. However, the Law of large number says sample mean converges in ...
15
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2answers
488 views

Intuition behind Box-Cox transform

For features that are heavily skewed, the Transformation technique is useful to stabilize variance, make the data more normal distribution-like, improve the validity of measures of association. I am ...
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0answers
20 views

Intuitive explanation for spline convolution [duplicate]

What is spline convolution intuitively? When should use it? what is the motivation behind it?

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