Questions tagged [randomness]

Randomness is the lack of pattern or predictability in events. Randomness is often modeled with probability distributions, but can also be generated by deterministic processes.

Filter by
Sorted by
Tagged with
0
votes
1answer
93 views

In Deep Learning, how much does randomness help generalization?

Let's assume at the beginning the NN is initialized with random weights, then the Backpropagation "shapes" the weights but the signal is strongest close to the final layer (where it gets computed) and ...
11
votes
2answers
738 views

Will this introduce bias into what should be random numbers?

Assume a data file with 80+ million ones and zeros, randomly generated. From this file, we want to create a list of random decimal integers. This is the plan to do this conversion. Divide the 80 ...
0
votes
1answer
15 views

Unsupervised learning problem: rate individual survey submissions on randomness of data entered

For my work we collect a lot of surveys which contain a mix of questions: multiple choice, checkbox and numeric. We know that in some instances enumerators might fudge the survey by entering answers ...
3
votes
1answer
68 views

Why does the law of large number hold for pseudorandom numbers

i`m wondering why the law of large numbers holds for pseudorandom numbers. Is this a empirical observation such as that the law of large numbers holds for coin tosses, or is this somehow programmed ...
1
vote
0answers
65 views

Simulating from the Gaussian Distribution

I attempted to sample random variables from the Gaussian distribution in C using the following simulation method: $$X_n = \sqrt{(-2\log(U_1)}\cos{(2\pi U_2)}$$ Where $U_1, U_2 \sim \mathcal{U}(0,\,...
2
votes
0answers
67 views

When random output is a local maximum, how can a neural network find the global (or a better local) maximum?

I'm trying to train a neural network to play Rock-Paper-Scissors. A random player is a local maximum for the game, as it wins 50% of the time. In a tournament setting, it comes out consistently ...
1
vote
1answer
38 views

Is there any way to derive the initial accuracy with random initialization?

In many iterative machine learning algorithms, weight/parameters are initialized as random. But is there any mathematical relationship between the random starting point and initial accuracy? For ...
3
votes
1answer
1k views

Testing for a Poisson process

Q1. I want to test if my data are the result of a Poisson process. I need to check if: (1) The number of arrivals N(t) in a subinterval of length t obeys the Poisson(λt) distribution or (2) The inter-...
0
votes
0answers
114 views

Random numbers without pre-specified distribution (revised)

I am trying to simulate the diet of the participants of an observational cohort (say n=10,000 - but could be larger). The purpose is two-fold: first I would like to use this to test some scripts, but ...
0
votes
1answer
180 views

What is the probability that a coin is a loaded coin?

If you randomly pick a coin from a box that contains $90\%$ fair coins and $10\%$ loaded coins, (a loaded coin gives heads $90\%$ of the time), toss it $5$ times and get all heads. What is the ...
0
votes
0answers
34 views

What is wrong with this self-made array shuffling algorithm? [duplicate]

I'm aware of the established array-shuffling algorithms, such as Knuth-Fisher-Yates. I'm interested in proving (or disproving) that my self-made shuffling algorithm is broken. It seems to be the ...
2
votes
1answer
95 views

Occurrence of at least 1 HT and HH in sequences of 4 coin flips not equally likely

I was reading this interesting article on hot hands and streaks in sports. The article revolves around the 16 possible sequences of 4 coin flips (H = heads, T = tails): ...
0
votes
1answer
39 views

Probability of homework being graded?

Say you have a class with 15 assignments. Over the course of the semester the teacher randomly choses 5 assignments to grade. The teacher also wants to keep it a surprise, that means the first ...
1
vote
0answers
87 views

purpose of random experiments in Jaynes' Baysian probability theory?

NOTE: I understand the role of random experiments in orthodox probability theory, and its role in providing unbiased estimators and hypothesis tests. Please don't answer this question with basic ...
1
vote
2answers
367 views

Methods of preventing overfitting other than adding noise to data?

I am about to begin running a data science competition. I have built a "baseline" model to test how accurate some of the competitors' submissions may be (I've set the target as to what they should aim ...
1
vote
0answers
66 views

the length of a random walk in two dimensions

This is a matlab code that could generate a random walk in two dimensions of length 1000: xy = cumsum (-1+2*rand(1000,2),1). The 'stepsize' is between $[-1,1]$. In this case, we are talking about ...
5
votes
2answers
695 views

What is the probability of selecting all the blue balls?

We have a bag full of many balls (let's say n balls). We cannot see inside of the bag but we are certain that only a certain number of them are blue (let say ...
1
vote
1answer
114 views

Confusion about measure theoretic approach of probability

Consider the case when someone starts with a random number $X$, then generates consecutive numbers by the recurrence relation $X = X + 1$. The measure-theoretic approach of probability states that if ...
5
votes
1answer
87 views

Does permutation permute also dependence?

I have a random vector $X = (X_1, \ldots, X_n)$ jointly distributed in someway, assuming also some mutual dependence between its marginal variables. If I apply a permutation to the vectors drawn from ...
2
votes
2answers
55 views

Taking two sets (A, B) out of the same distribution, merging and then sorting should roughly result in a,b,a,b,a,b?

Suppose I take 2 sets ($A$ and $B$) of 1000 random items out the same distribution; I also suppose that all items are different. I then create a new set $C$ which is the union of $A$ and $B$, since ...
1
vote
1answer
990 views

XGBoost - “Optimizing Random Seed”

I have just started working with xgboost in python am pleased how its working and have just begun optimizing my model. Without going into to much detail, my model uses XGBClassifier to predict a ...
3
votes
4answers
1k views

Is the Intersection Area Between 2 PDFs a Probability?

Say that we have two processes $a$ and $b$ that generate numbers. Then say that the random variables $A$ and $B$ take values in the set of numbers that those processes generate, respectively. So $f_A$ ...
0
votes
1answer
267 views

What do we mean by “Random” in the science's context

What do we mean by 'Random' in the science's context. Especially in the statistics and signals processing field. I looked to the dictionary definition of Random and this is what I found: Made, done, ...
1
vote
0answers
64 views

Comparing the performance of random and weighted-random classifiers

I have a set of 300 observations of known class and there are 20 classes in total. I want to compare the performance of a random classifier with a weighted-random classifier at classifying the ...
1
vote
0answers
324 views

Uniformity of true random numbers

Are numbers generated by True (hardware) Random Number Generators (TRNGs) more uniform than numbers from a Pseudo Random Number Generator (PRNG)? I understand that there are not much (analytical/...
0
votes
1answer
71 views

Choosing the best method to test how random are P/RNGs [duplicate]

[1] I'm testing some P/RNGs algorithms, so in order to see how normally distributed are the values obtained by these Random Number Generators (resp. Pseudo-), which method suits best? Is drawing the ...
0
votes
1answer
48 views

Is it random to split ordered data on every ith entry?

I have an ordered set of data, X, that I want to split into a 10 random groups to do 10-fold cross validation. The data set is very simple with one feature per row. I am wondering if it is random/...
2
votes
1answer
357 views

What is the difference between a Lag plot and a Poincare plot?

So I recently came across Poincaré plots (Wiki) which plots x(t) against x(t+1). Thereafter I found out about lag plots (Description)which seem to do the same thing just the other way around, i.e. x(t)...
0
votes
1answer
96 views

Single index to measure the randomness of multivariate distributions (or data)

Are there any single indices to roughly measure the degree of total randomness of a multivariate distribution (or data)? For example, assuming I know the covariance matrix $S$ of a multivariate ...
2
votes
2answers
100 views

Check whether data set is ether randomly generated, biased or “too uniform”

I have a data set with data from 26 multiple-choice exam papers. Each question has four alternatives, one of which is correct. I know, for each paper, how many answers had A as the correct option (...
1
vote
0answers
603 views

How to do cross validation in Random Forest if the objective is to measure variable importance?

As you know, the random forest algorithm and k-fold cross validation (except the case of Leave One Out) involve randomness. Thus a typical 10-fold CV in one run results in a certain variable ...
1
vote
0answers
23 views

What's the best method for figuring out whether clusters occurring in data are random or are indicative of an underlying non-random behavior?

I have a dataset of the times that events happen. I noticed some clustering of events but I know that even assuming a random uniform distribution some amount clustering will inevitably occur. How do I ...
3
votes
1answer
340 views

Is it true to say that (pseudo) random variables generated by a deterministic procedure must be correlated in some sense? why?

Suppose I have a pseudo random generator rand, I am using it to generate two random variables X and Y as follows: ...
0
votes
2answers
176 views

Is this a reverse Birthday Problem problem? [duplicate]

I have a machine that generates 16 character long sentences made up of (I think kinda) random letters. I can get it to spit out up to 1 million such sentences before I loose the ability to store them (...
1
vote
0answers
48 views

Detecting extent of randomness of a binary time series

I have several time series that take a value of 1 if an event occurs and 0 otherwise. I would like to measure randomness of each time series is. What would be a good measure for this? The reason I am ...
9
votes
3answers
527 views

High autocorrelation when taking the L-th order of difference of a sequence of independent random numbers

To explain this question in more detail, I'll first elaborate my approach: I simulated a sequence of independent random numbers $X = \{x_1,...,x_N\}$. I then take $L$ times the difference; i.e. I ...
3
votes
2answers
1k views

Interpreting the results of two tests of randomness

I have a series of more than 1000 numbers which are not supposed to exhibit any particular trend, regularity or non randomness. The numbers are the results of tests for the presence of substances in ...
1
vote
0answers
72 views

Variation of Wald–Wolfowitz detecting seasonal patterns?

I am considering the standard test for randomness based on runs(Wald–Wolfowitz runs test). In it, you basically take a sequence of 1's and 2's, having length $n$, $n_1$ 1's, $n_2$ 2's and you want to ...
1
vote
0answers
66 views

How can I test if a string on distinct numbers/characters is random?

Let's say I have a string of 26 letters. I want to permute them and then test if my permutation is random. How do I do this?
31
votes
5answers
8k views

Generating random numbers manually

How can I manually generate a random number from a given distribution, as for instance, 10 realisations from the standard normal distribution?
4
votes
1answer
304 views

Likelihood function and Fisher information of a coin experiment

I'm trying to understand the notions of likelihood function and Fisher information with a simple example. Suppose I have a coin that gives 0 with probability $p$ and 1 with probability $(1-p)$. I've ...
1
vote
1answer
37 views

Calculation if results of model ranking could occur by chance alone

I have a prediction tool which ranks 56 models of proteins based on computation. I also have the correct ranking of those structures based on the closeness to actual structure of the protein. If I ...
0
votes
0answers
22 views

Tools to measure the nonrandomness of databases [duplicate]

I was working on historical data looking for anomalous patterns that we would not expect to occur at random. I'd like to create a scheme to analyze data and markets to test for statistical ...
4
votes
1answer
253 views

I cannot understand the definition of order statistics

From G. Casella & R. Berger "Statistical Inference": Definition 5.4.1 The order statistics of a random sample $X_1,\dots,X_n$ are the sample values placed in ascending order. They are denoted ...
22
votes
7answers
7k views

Can someone help to explain the difference between independent and random?

In statistics, does independent and random describe the same characteristics? What's the difference between them? We often come across the description like "two independent random variables" or "...
3
votes
0answers
64 views

A pseudorandom number generator with a seed greater than 80 bits

I need to generate a sequence of pseudorandom numbers with a period larger than $2^{80}$, using a seed larger than 80 bits, on a 32-bit embedded microprocessor. What are my possible options (in terms ...
4
votes
1answer
1k views

Is it valid to use latin-hypercube sampling in parallel sampling?

I am sampling from a model 10 times in series, doing this in 50 parallel processes. I am using LHS to generate samples each set of ten samples, although each of the 50 parallel runs' samples are ...
1
vote
1answer
368 views

Statistical test for cross-correlation

Is there any statistical test to determine that two sequence of numbers (e.g. numbers generated by uniform pseudorandom number generators) have a good cross-correlation (close to zero for all lags) ...
5
votes
2answers
766 views

How to efficiently choose $n$ subset out of a set of $m$ many numbers, in a randomized uniform manner?

Problems: It is fairly simple: we have a list of numbers $x_1, x_2, \ldots,x_n,\ldots, x_m$. Our goal is to randomly and uniformly choose a subset of $n$ many numbers out of these. This means that, ...
0
votes
0answers
29 views

Formal proof that a subsample of a random sample is representative [duplicate]

There are two questions asking about the random nature of a subsample (here and here). However, they do not provide a formal proof of the result. I am looking for a proof to support my selection ...