Questions tagged [references]

Questions seeking external references (books, papers, etc.) about a particular subject. Always use a more specific tag in addition.

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What is a “surface” and the “likelihood”?

On Neyman & Pearson, 1933, page 302, Then the family of surfaces of constant likelihood, $\lambda$, appropriate for testing a simple hypothesis $H_0$ is defined by $$ p_0 = \lambda p(\...
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18 views

Understanding the general theory proposed by Neyman & Pearson

I'm reading Neyman & Pearson, 1933, i.e. Neyman and Pearson. On the problem of the most efficient tests of statistical hypotheses. Philosophical Transactions of the Royal Society of London. ...
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1answer
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Test of ratio within population

Let's say I have two large containers, X and Y, both containing a mix of red and blue buttons (for clothes). Consider the unknown ratios $x$ := #blue / (#blue + #red) in container X $y$ := #blue / (#...
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18 views

Citation for minibatch processing?

Kind of a silly question, but is there a paper which first introduced minibatching?
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Does family of sufficient $\sigma$-subalgebras depend on the reference measure?

Let $\{ P_{\gamma} \}$ be a parametric family of probability measures on $(\Omega, \mathcal{F})$, such that $P_{\gamma} \ll \mu$ for all $\gamma$, for some $\sigma$-finite $\mu$. Consider the Radon-...
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What are some examples of reversed usage of “percentiles”?

The technical definition of a "percentile" in statistics is taken from the quantile function; it is the value below (or below or equal to) which a given percentage of values falls. For example, the ...
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33 views

Sufficient statistic for Gaussian $AR(1)$

Question Does the Gaussian $AR(1)$ model, with a fixed sample size $T$, have nontrivial sufficient statistics? The model is given by $$ y_t = \rho y_{t-1}, \, t = 1, \cdots, T, \; \epsilon_i \...
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Undefined terms in van der Vaart's Asymptotic Statistics: “statistic in the experiment” and “convergence in distribution under the parameter” [on hold]

The phrases below (in bold) appear in van der Vaart's "Asymptotic Statistics" and are used repeatedly in theorem statements. (This is from Ch. 7 on local asymptotic normality.) What do they mean? The ...
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28 views

Gaussian sufficient statistic calculation

Consider the Gaussian model $$ Y_i = \beta + \epsilon_i,\, i = 1, \cdots, n,\; \mbox{where}\; \epsilon_i \stackrel{i.i.d.}{\sim} \mathcal{N}(0, \sigma^2), $$ parametrized by $\beta$, with known $\...
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GANs for non image data

I'm looking to narrow down the subject for my bachelor thesis: I am currently working on a project, that only offers a small dataset and there will be no more data incoming for now. What I'm trying to ...
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48 views

Time Series and regression analysis online course

I am going to pursue my PhD in Data Science. My BS and MS degrees are in Mathematics. I would like to learn some self-paced statistics online courses to make my PhD journey more comfortable. I never ...
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1answer
28 views

Generalized linear model (GLM) for panel data?

I have a panel data and what I need is to use generalized linear model (GLM), but I am confused; that is, I cannot find any related article in which they have used GLM for panel data. Can you share ...
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Reference Request - Comparing deep learning books

There are multiple books on deep learning currently available. I'm primarily interested in the theory and algorithms and less interested in the "practical guide" books really just tell me how to use a ...
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Best book for theory of probability and statistics [duplicate]

I need a proof based book to study theory of probability and statistics. I have read that one of the best is Mood & Graybill. I just want that it is proof-based, rigurous, and it talks about ...
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book recommendation - statistics in medicine

Could you recommend a book about the implementation of basic statistic concepts in medicine? In particular, I want to find a book that covers principal component analysis, correspondence analysis and ...
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36 views

Reference request - Computer Vision Book

What are the best books for obtaining a strong understanding of computer vision? From what I understand based on my undergraduate class, almost all current state-of-the-art computer vision is just ...
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28 views

Comparisons of targeting models

I need to compare two targeting models in an experiment. We will apply the same treatment to everyone who is targeted. The experimental set up is as follows: The total population is split into ...
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10 views

Reference for Inception-v2

Cross-posted from Data Science StackExchange. The "Rethinking" paper doesn't describe the actual implementation of the Inception-v3 model in Tensorflow: an accurate description is written in model....
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183 views

Argument on Interactions in The Book of Why

There is a paragraph on interactions in The Book of Why (Pearl & Mackenzie, 2018), Chapter 9 (I cannot share the page number because I have the book in epub format), where the authors argue that: ...
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Reference Request: Overall and Average Accuracy [duplicate]

I am looking for a source to cite on the definitions of overall and average accuracy. I have found many informal sources online, including here on CVSE, but the papers and textbooks I have found seem ...
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1answer
25 views

Theory on custom loss functions for GBDT and other ML

I'm looking for resources on the theory behind choosing a loss function for ML---I'm interested in GBDT but for deep learning would work as well. I'd like to get a better understanding of how the loss ...
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22 views

Reference request: Network/graph topology inference

I am a mathematician looking for a survey/book on methods for inference of graph/network topology (structure). Specifically, the kind of problem I am looking to study is as follows: Given a graph $...
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1answer
23 views

Standardized residuals GARCH models

Lets say I have a GARCH(1,1) model, First, I model the conditional MEAN, $$Y_t=\delta+\beta Y_{t-1}+\varepsilon_t$$ NextI gather the residuals $\varepsilon_t$ and model the conditional variance, ...
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2answers
35 views

Applying TF/IDF to non-text data?

I have a classification problem in which I am supposed to predict the end state of an object based on a set of events it experiences. There are about one thousand possible events and each object is ...
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1answer
48 views

Reference for continuous (multivariate) distributions?

A reference that not just enlist the formulas of continuous (multivariate) distributions but goes in details about them and maybe treat the relations between them (e.g. derivation/proofs, intuition ...
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MSE series derived from cross validation on time series

This answer suggests a way of doing leave-one-out cross-validation on time series data: An approach that's sometimes more principled for time series is forward chaining, where your procedure ...
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Name and interpretation of “$h(x)$” in exponential family

The exponential family is defined (in many sources) as: $$p(x | \theta) = h(x) \exp\{\theta^TT(x) - A(\theta)\}$$ where: $T(x)$ is a sufficient statistic, $\theta$ is a canonical parameter, and $A(...
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Distribution Reference $\gamma x^{\gamma-1}$

I have been unable to find resources regarding the family of distributions with pdf $$ f_\gamma(x) = \begin{cases} \gamma x^{\gamma-1}, & \text{if } 0 \leq x \leq 1 \\ 0, & \text{...
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37 views

Generalizing Bayesian methods by assuming a “distribution of distributions” instead of a prior

Bayesian methods assume a prior distribution with several hyperparameters. Unfortunately, this is asymptotically incorrect, because distributions in the real world are never exact. For example, the ...
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A book-chapter long nontechnical introduction / overview of neural networks

I will be teaching an introductory course in machine learning for students in management who have minimal quantitative skills. I am looking for a brief and gentle introduction to neural networks that ...
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1answer
24 views

applied papers on probabilistic generative models and inference engines

I am looking for applications papers where people choose some task on which they will do Bayesian inferencing and graphical modeling, and then build an inference engine to infer latent parameters. And ...
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What are the main approaches to the foundation of statistics without probability

The frequentist, likelihood and, to an even greater extent, Bayesian approaches to statistics are all based on probability. Without probability, it seems difficult to use a data sample ("seen" cases), ...
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Probability of sparse spectrum

Consider a vector $v$ such that $v \sim \mathrm{Unif}(\mathbb{S}^{d-1})$, the uniform distribution on the unit sphere in $d$ dimensions. Question: is there an upper bound on the probability that $v$ ...
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Convergence rate of the inverse covariance matrix [closed]

I am trying to find results regarding the convergence rate of the inverse covariance matrix in the case where the number of observations $n$ is larger than the number of dimensions $p$. Assume that $...
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26 views

Alternatives to The Statistical Sleuth?

I am looking for a simple and concise book on statistics (t-test, ANOVA and all its variants, liner regression, etc.), centered on data analysis. I am not interested in theory or proofs, but just want ...
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19 views

Dimension of a probability distribution function

Consider the following statement We want to sample from a complex high dimensional distribution which is intractable. What is meant by a dimension of distribution here? Does each random variable ...
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1answer
22 views

How much matrix differentiation background for Seber and Lee's Linear Regression Analysis

How self-contained is Seber & Lee's textbook 'Linear Regression Analysis'? It seems to assume knowledge of matrix differentiation.
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Does a more powerful test mechanically lead to more type III errors then?

"Type III error occurs when you correctly conclude that the two groups are statistically different, but you are wrong about the direction of the difference. Say that a treatment increases some ...
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Literature on conceptual understanding of beta regression

I am researching beta regression models to decide if they are appropriate for my data. My very first search yielded this basic introduction, that also describes the zero-one inflated beta regression. ...
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Literature recommendation for convolutional neural nets

I am looking for a good book or an article concearning convolutional neural nets, especially their architecture. I like the http://deeplearningbook.org but it does not provide any information on the ...
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43 views

Targeted Maximum Likelihood Estimation for dummies?

I have tried to get my head around the concept of TMLE, but most references seem to be written by people who despise being understood (or maybe I am just hebetudinous). I have tried to read the paper ...
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References for this ARMA two step method estimation

I was doing some survey on ARMA parameters estimation methods. While on that, I found these lecture notes: http://www.phdeconomics.sssup.it/documents/Lesson12.pdf There, the author describes a two ...
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1answer
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Gradually increasing reinforcement learning environment complexity

The problem of robotic arm control has different levels of complexity ranging from simulation to real-world application. For example, a simulation may not model friction of the joints, which becomes ...
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1answer
24 views

When kernels are not useful in SVM?

In SVM using kernels we map the original features to the higher, transformer space (feature mapping) and then perform linear SVM in this higher space. But when kernels are not useful? I could not find ...
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31 views

Mysteries of the Normal Distribution [duplicate]

I have been studying ML for over a year and am actually a Bachelors of Statistics myself and am sick of not knowing the beauty of the Gaussian distribution and why it is so prevalent in nature. I've ...
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1answer
43 views

Why is using keras ImageDataGenerator for data augmentation relevent?

I have used keras ImageDataGenerator to generate more data in my neural networks as I have had really small datasets and it has proven itself. As far as I ...
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1answer
145 views

Analysis of count data with percentages

for my master thesis I count and identify sediment grains. In total I have 82 samples from 3 different gravity cores. I divided the sediment components in 11 groups (Quarz, Mica, Opaque, Aggregate, ...
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How to combine noisy and noise-free datasets to train a model

Overview Suppose I have two datasets, both of which consist of rows of features and their matching labels. One of these datasets is noise-free and its labels correspond to the ground truth, but the ...
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2answers
97 views

Are GLMs just glorified WLS regressions?

When performing weighted least squares $L = \frac{1}{2} \sum_i w_i r_i^2$, Aitken showed that one ought to weight each sample by the inverse of its variance $w_i=1/\sigma_i^2$. This leads to gradients ...
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Dealing with extreme outliers in administrative data (in R)

I work with some data that includes some "extreme outliers". E.g. timestamps that are totally unreasonable (surgery took 20 days when most take 1 hour). Is there a set of principles one can use to ...