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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References for BERT training from scratch

As the title of the question suggests, I'm interested in training a BERT-like model (and then use it to make some experiments on text-similarity). Question: Could you share some references on the ...
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4 votes
2 answers
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What are the k-means algorithm assumptions?

I'm trying to understand what are the assumptions/hypothesis underlying the k-means clustering algorythm; specifically, I'm looking for a research/academic paper listing such hypothesis and explaining ...
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List of Statistics/Data Science journals with a tier/quality/class indicator [closed]

I have been looking at different sources to collect a list of Statistics or Data Science journals (including machine learning journals or methodological journals like Nature Methods and Bioinformatics)...
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Limit distribution of the joint distribution of maximum and minimum of a sequence of random variables

Assume we have a sequence $\mathsf{X}_1,\mathsf{X}_2,\mathsf{X}_3,...$ of iid random variables. Then the Fisher-Tippet-Gnedenko theorem shows that $$ \mathbb{P}\left(\frac{\max\{\mathsf{X}_1,\mathsf{X}...
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2 answers
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Objective criteria for assumption violations that do not utilize p-values?

Suppose we have a standard regression model and want to identify whether we have violated the assumptions of the model. Traditionally, we might utilize a significance test to determine whether (for ...
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References for cross-validation implementations in Pytorch

I'm interested in good references on cross-validation implementations for feed-forward neural networks in pytorch from scratch. Thanks in advance.
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Is there a statistic such that for large sample sizes $a_n (\hat{\theta} - \theta) \sim N(0, \Sigma)$ approximately but $a_n \neq n^{1/2}$?

Various central limit theorems are of the form $a_n(\hat{\theta}-\theta)\sim N(0, \Sigma)$ approximately as $n \to \infty$ and usually $a_n = n^{1/2}$. Are there central limit theorems for statistics ...
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Does Geyer's mode selection heuristic perform no-worse than burn-in?

In Charles Geyer's Burn-In is Unnecessary he writes Another possible rule is to start at a point, like the mode, known to have reasonably high probability. If no such point is known, this rule is ...
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Formal approach to message passing algorithms

I'm trying to understand message passing algorithms, especially for the specific application of performing conditioning in a Bayesian network. My question is wether there is a mathematically precise ...
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Book recommdations for reinforcement learning [duplicate]

I recently read Learning from data by Abu Mostafa. Can someone recommend a book focused on reinforcement learning which is just as mathematically rigorous as learning from data?
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2 votes
1 answer
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Proof that a necessary condition for characteristic roots to lie inside unit circle is $\sum\limits_{i=1}^{n} a_{1} < 1$

I have been trying to show that given $$P_{n}(\alpha) = \alpha^{n} - a_{1}\alpha_{n-1} - a_{2}\alpha^{n-2}... - a_{n} = 0,$$ the $\alpha$'s that solve this equation (real-valued or complex) lie in the ...
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What is a good introductory guide to Bayesian MCMC Analysis in R?

I am trying to perform Bayesian Analysis in R, using of Monte Carlo Markov Chains to calculate the probability of, in a set of data, there being a gaussian peak at a certain location $x_0$ (my 'target'...
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What important ideas came since Nelder and McCullagh's book Generalized Linear Models (a 40 year old book)?

I read not too long ago Nelder and McCullagh's book Generalized Linear Models and thought the book was fantastic and I consider it a useful manual on the subject. Not surprising that's the case, ...
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Source for KL-divergence of Beta distribution?

This post explains how to derive the Kullback-Leibler divergence between two beta distributions. https://math.stackexchange.com/questions/257821/kullback-liebler-divergence#comment564291_257821 I ...
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1 answer
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How to tell if my features improve model performance?

Setup Task: binary classification Models: logistic regression, SVM, ELM, neural networks - anything that can do classification Dataset: 10 basic features + 6 my own features Question How do I see ...
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How to interpret the coefficients in robust weighted Tobit regression model?

I am looking for any reference helping explaining the coefficients in Tobit model for beginner. I found a topic in our exchange but it seems still not clear to me. I am finding a handy reference like ...
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1 answer
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3D convolutions and jitter

I want to process a sequence of cropped and aligned face images from a video with a neural network. I am considering a use of 3D convolutions in order to capture the spatiotemporal dependency. However,...
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1 vote
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Good example of a walk-through of the FCI algorithm to ensure all steps are done

The FCI algorithm is a common algorithm used for learning a Markov equivalence class of causal graphs from observational data. I am wondering if there are any good examples that walk through a causal ...
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7 votes
3 answers
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Test the hypothesis that the performances of k machine learning models on the same test set is the same

I have $k$ Machine Learning models, trained on the same training set, and I want to test the hypothesis that their performance on a fresh test set is the same. See EDIT 1 below for what I mean with ...
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4 votes
2 answers
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Determining spline basis dimension using Wood's statistical test

In Simon Wood's book Generalized Additive Models (2nd ed.) on page 243, he describes the following procedure for checking that the basis dimension is too small: Fortunately informal checking that the ...
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3 votes
1 answer
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How does removal of symmetry (e.g. via constraints) in a Bayesian optimization search space affect search efficiency?

There are many examples of search space symmetry in real-world optimization problems in the physical sciences. To motivate this, here are some that come to mind: When optimizing a formulation such as ...
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2 votes
0 answers
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Supplementary material for "Survival and Event History Analysis, A Process Point of View" by Aalen et al

I am doing a self study of "Survival and Event History Analysis" by Aalen et al. Overall, I like the book. It is my second pass at survival analysis (I used Survival analysis: Techniques for ...
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Construction and validation of an index

We use different methods to construct indices for different things, say the Human Development Index, the Consumer Price Index, Democracy Index etc. These indices seem to have quite different ...
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Resources to help a recent statistics graduate deal with real world statistical problems

I recently got my master's in biostatistics, so I know the basics. However in my work there are many situations where people ask me "would it be statistically valid to do xyz" and I really ...
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Lecture notes for the dip test

Are there any good lecture notes/textbook/exposition article that explains the Hartigans' dip test of unimodality? I have seen the original paper but I was wondering if there are any other learning ...
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Citable references for change of variables of probability distributions

I would like to cite a paper or book etc (and the older the better) that demonstrates basic change of variables for probability distributions. Web searches are fruitless - it seems the technique is so ...
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2 answers
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Why can't we just add a penalty to make the Neural Network objective convex?

When we use Neural Networks to solve various tasks, we define an objective that the Network parameters $\theta=(\theta_i)_{1\le i\le N}\in\Theta^N$ have to minimize. So, for neural networks $f(\cdot|\...
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1 vote
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On the naming of two different median estimators

Assume that $X \sim \mathcal{E}(\lambda)$ is, for example, exponential with $\lambda > 0$. Given a data sample $X_1, \ldots, X_n$, assume that I want to estimate the median of $X$. Consider these ...
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Practical statistical course advice [closed]

Can you please advise me about a good online statistical course with practical examples in R that can help me to be confident when I'm doing my analysis. I have basic to intermediate knowledge in ...
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Reference for calculating $R^2$ on a subset of the samples

I've been looking for a method to calculate $R^2$ on a subset of the samples (a subset of the instances, not a subset of features), and found this answer from Dave. It suggests using the mean of the ...
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Suggestions of Statistics and Time-Series Books

First of all, Im not new to the topic but I have lost time searching for Statistics and Time-Series books with Math background + Algorithms and that are Code-Only and worse, Libraries usage. I'm ...
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Non-parametric joint difference in means between groups

Background: I want to test the difference in means between two groups along multiple variables. The approach I know is to run a regression where the group variable defining the populations is the ...
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1 vote
1 answer
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Do neural networks with similar weights necessarily compute similar functions?

Let $f_1(\cdot|\Theta_1)$ and $f_2(\cdot|\Theta_2)$ be two Feedforward Neural Networks with the same architectures (number of layers, width of each layer, activation function...) and parameter arrays $...
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Targeted Learning in Data Science: background material

I am interested in the use of modern causal inference methods to research the association between a (non-genetic) exposure, and endogenous molecules and/or health outcomes (high-dimensional data). I ...
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1 vote
2 answers
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The P-value as the expectation of an indicator function

I am familiar with the notion that $Pr(A) = \mathbb{E}[1_{\omega \in A}(\omega)]$, given some suitable measure theoretic assumptions. I seem to recall a comment on a ...
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Standard Deviation of normal distribution transformation - Wilcox book explanation

I started reading the book of Rand Wilcox "Introduction to Robust Estimation and Hypothesis testing" (4th Edition). In the first chapter of the book, it is written: Let $X$ be a standard ...
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1 vote
1 answer
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Who proposed the reflective correlation coefficient?

The Wikipedia page for the Pearson product-moment correlation coefficient has a section on variants of the idea. This includes the reflective correlation coefficient, which has had a citation needed ...
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Friendly reference for point estimation that covers the following

I took a mathematical statistics class in college which covered the following: Cramér–Rao bound Lehmann–Scheffé theorem Rao–Blackwell theorem I found these theorems very beautiful and want to ...
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How to design a method for finding multiword terms based on labeled data

Setup: I have many textdocuments that have been processed by an OCR Engine. These documents are Invoices and the endgoal is to classify words inside each document. If words on a document are seperated ...
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0 votes
1 answer
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Metric to measure how "standard Gaussian" a set of samples is?

Assume that I have a set of $N\in\mathbb{R}^{D}$ samples from some otherwise unknown multivariate distribution $p$. I seek a metric which might tell me how "close" $p$ is to a standard ...
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1 vote
2 answers
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How to handle assumptions of statistical tests?

Does any definitive work exist, e.g. a review, a book chapter, or a book, on the advantages and disadvantages of existing approaches? Is there a consensus on which approach is the right one? I have ...
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Muticategorical predictor Model 1 PROCESS

I am trying to find resources on how to interpret and write up the results of analyses using PROCESS Model 1 with a multicategorical predictor (X) and a continuous moderator (M) and continuous outcome ...
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Reference request: introducing Granger Causality

I have just read Granger Causality off the internet, but have not managed to read it from authoritative texts. I want to request for textbooks that introduce this important concept, applied in the ...
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When is the existence and/or unicity of the Empirical Risk Minimizer guaranteed?

In Supervised Machine Learning, it is common to learn a target function by minimizing a (regularized) Empirical Risk Objective, i.e., for a dataset of $n$ samples $(X_i,y_i)$, the learned function $\...
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1 answer
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Combining earnings report data with customer satisfaction survey data

There is a popular Kaggle dataset on airline CSAT. It is a customer satisfaction survey using features of inflight services and travel procedures such as ...
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1 vote
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What are some recommended Graduate-Level Probability and/or Statistics textbooks for an incoming Econ PhD Student?

Title covers most of it. I'm an undergrad who will be graduating in a few weeks and will be starting a PhD Program in Economics. I'm interested in Econometric theory. I've taken undergrad level ...
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Resources on Modeling Regional Count/Rates

I'm looking into the time-evolution of regional count data. The real target is modeling death rates at the county level over time. I was wondering if people had suggestions on where to start reading ...
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What are some good papers/books I could use in my thesis? [duplicate]

In the literature overview part of my thesis I have some chapters regarding time-series: -Introducing time-series analysis (sub-chapter: time-series on stocks) -Limitations, disadvantages and ...
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1 answer
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Difference between Predictive Inference and Causal Inference

I am looking for functional mathematical notation to explain the difference between Predictive Inference and Causal Inference? I list an example model. I also list links further down that give ...
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How to reveal specific relationship using tSNE?

I’ve been using tSNE in attempts of finding and visualising some relationships in my data. I came to a following problem. If my data is say 1000 points, and I want to know about some relations between ...
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