Questions tagged [statistics]
The statistics tag has no usage guidance.
153
questions
0
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30
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Impact of label flipping on ROC-AUC score
I was exploring a problem of label flipping in the target column:
Problem:
I have a data frame with just two columns: Predicted probability | Target. Target column is binary (contains only 0 and 1) ---...
- 95
0
votes
2
answers
123
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Minimum number of comparisons to find $2$nd smallest element
Show that the second smallest of $n$ elements can be found with $n+\lceil\lg n\rceil-2$
comparisons in the worst case. (Hint: Also find the smallest element.) [1]
I tried but I have no idea how to, e....
- 129
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votes
1
answer
32
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Finding the mode of a continuous distribution
I need to find the empirical mode of a sample of numbers taken from a continuous distribution (i.e. floating-point data).
I can think of using an histogram, but choosing an appropriate bin size does ...
user16034
2
votes
0
answers
24
views
Sample Complexity Lower bound for PCA
I am trying to find (without success) a sample complexity lower bound for PCA. The concrete problem I am considering is -
$X_{1}, X_{2}, \cdots X_{n} \sim D(0, \Sigma)$ are $d$-dimensional vectors ...
-1
votes
1
answer
52
views
How to calculate the growth function of a hypothesis class?
I have this hypothesis class:
H = {ha : R → {0, 1} | a > 0, a ∈ R, where ha(x) = 1−a,a =
{ 1, x ∈ [−a, a]
0, x ̸ ∈ [−a, a] }
I need to compute the growth function for m>= 0. So I think that this ...
- 1
0
votes
2
answers
67
views
Bucket sort for gaussian / standard distribution
I know this post. But I still have no idea to adapt the bucket sort algorithm to handle input with a gaussian / normal distribution. Can someone provide me a Pseudocode / Python code for that? So far ...
- 121
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0
answers
5
views
Reproducible research (published papers) about e-commerce or fashion
I am looking for reproducible research (published papers) about e-commerce and/or fashion which deals with exploratory data analysis, hypothesis testing and regression or ANOVA. This reproducible ...
- 1
0
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0
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60
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How to extend an existing Monte Carlo method and to add new constraint
Currently I'm trying to extend an existing Monte Carlo model to simulate the process of production line that produce rolls of paper under some conditions, and to ...
- 1
1
vote
3
answers
98
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What set.seed() mean in the Monte Carlo method
I'm trying to learn the implementation of the Monte Carlo method in R language. I am following a course with an example of predicting results for a board game. What I'm not understanding is the usage ...
- 11
1
vote
2
answers
72
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Why use Welford's Method over a more naive approach?
I came across this pair of blog posts explaining the problem with calculating variance on floating point data:
https://jvns.ca/blog/2023/01/13/examples-of-floating-point-problems/#example-3-a-variance-...
- 111
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0
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18
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What is the advantage of every Bayes Nets Sampling algorithm?
I have studied four Bayes Nets Sampling algorithms for calculating the probabilities, including:
$1. Prior Sampling$
$2. Rejection Sampling$
$3. Likelihood Weighting$
$4. Gibbs Sampling$
And my ...
0
votes
0
answers
31
views
How to create random pseudo samples from a non-stationary time series containing NaNs using Monte-Carlo method?
I am looking for answers creating 500 samples of non-stationary Time series based on its probability distribution preferably using monte-carlo simulation. DATA LINK
Secondly, the most example ...
- 1
1
vote
1
answer
62
views
Efficient algorithm for finding linear combination of piecewise functions
While porting an algorithm, I having a bit of a problem with finding an efficient algorithm for finding a linear combination of piecewise functions. The procedure is described in the Table 3 of the ...
- 113
1
vote
1
answer
43
views
Naïve array sampling algorithm: the possibility of a item being chosen and its time complexity
This naïve sampling algorithm I am talking about is fairly simple: create a set for storing chosen items first, randomly select an item from the array, and examminate if it is in the set. If it isn't, ...
- 111
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0
answers
29
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Tight bounds for expected maximum of k binomial(n,p) IIDs
What is the tightest lower and upper bound for the expected maximum value of k IID Binomial(n, p) random variables
I tried to derive it :
$$Pr[max \leq C] = (\sum_{i = 0}^C {n \choose i}p^i(1 - p)^i)^...
- 13
1
vote
1
answer
33
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Distribution maximizing ratio of expected maximum over the mean
I’m looking for a distribution that is non-negative, or has good tail bounds (so non-negative with high probability) and maximizes the ratio between the expected maximum of $n$ iid samples and the ...
- 13
3
votes
0
answers
63
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Algorithm for half-sample mode better than O(N^2)
The half-sample mode is a mode estimator that homes in on the highest density region of a set of samples in search of the mode. It is one of the better mode estimators, though it fails for J-shaped ...
- 251
1
vote
0
answers
39
views
Precise definition of Universal Learner in Machine Learning
It is surprising to me that I cannot find a precise definition of universal learner on the internet. I can guess what it should bebut I don't want to make a mistake, therefore I have come here.
Here's ...
- 11
1
vote
0
answers
102
views
Hoeffding's inequality applicability for sample complexity
I am trying to determine some bounds for sample complexity. Suppose we have a bounded loss function $\ell$ and target function $f:\mathcal{X}\to\mathcal{Y}$. Hypothesis $h$ is learned, then the ...
- 11
1
vote
0
answers
134
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Computational complexity of median filter in image processing
I found this paper http://nomis80.org/ctmf.pdf, that describes an efficient algorithm for applying a median filter to an image. Though this works for non-HDR images, I am not sure how well it scales ...
- 147
4
votes
2
answers
952
views
What empirical evidence do we have for or against a correlation between fault density and LOC?
LOC = lines of code
KLOC = Thousand lines of code
Fault (or defect) density = number of reported bugs per line of code.
Software artifact = function, class, module
Reading research papers on fault ...
- 375
0
votes
1
answer
65
views
Efficient random sampling from large discrete distribution
I have a random variable $X$ that can take finite values in $\{X_1, ..., X_n\}$ with probabilities $\{p_1,..., p_n\}$. Is there a computationally efficient way to sample a number from this set? My ...
- 3
1
vote
0
answers
13
views
Distributed Graph Consensus to fit a distribution?
$G$ is a strongly connected graph with nodes $V$ and edges $E$. Each node $v_i$ receives a sample $x_i$ from a Gaussian $\mathcal{N}(\mu,\sigma^2)$ with unknown mean and variance.
The objective is for ...
- 532
1
vote
0
answers
20
views
Distribution independence property testing
I have been reading the proof in the following paper, and I am unable to understand some parts in the proof. This paper shows that a distribution $A$ over $[n]\times[m]$, $n\geq m$, can be $\epsilon$-...
- 11
1
vote
2
answers
531
views
Sliding window max/min algorithm without dynamic allocations
I'm working on a suite of DSP tools in Rust, and one of the features of the library is a collection of windowed statistics (mean, RMS, min, max, median, etc) on streams of floating-point samples. For ...
- 173
1
vote
1
answer
51
views
EM algorithm - What happens with the standard deviation?
What have you tried?
So I watched this video.
According to the video, we've to calculate the variance $\sigma^2$ as follows:
$$
\sigma_{k}^{2} =
\frac
{
p_{1} \left(x_{1} -...
- 121
0
votes
1
answer
42
views
PCA applicability
I understand that PCA takes a data set with input size, with output labels, and reduces the inputs to a set of principal components size r, where r < n.
My question is whether or not this can be ...
- 5
0
votes
0
answers
120
views
Most popular path in weighted cylic directed graph
Context
I have a graph $G=(V,E)$ with weighted edges, all weights are positive integers $w(e)\in\mathbb{N}\setminus\{0\}$. The weights represent the popularity/count of each edge, for example $w(e) = ...
- 111
1
vote
1
answer
304
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Approximate max weight path in directed graph
Context
This question is related to the fact one can't use Bellman-Ford to find max weight paths in directed graphs with cycles. The reason is that giving a new graph $\tilde{G}$ with negative weights ...
- 111
0
votes
1
answer
308
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Chebyshev’s inequality problem in one exercises I can't understand if I did it right or not
This is what do I have to solve:
Byron Book: Exercise 8.3 chapter 8
Verify the use of Chebyshev’s inequality in (8.6) of Example 8.16. Show that if the population
mean is indeed 48.2333 and the ...
- 119
2
votes
0
answers
22
views
Separating labelled points with a plane, minimizing label variance
Suppose we have observations with associated labels $\{({\bf x}_1, y_1), ({\bf x}_2, y_2), \dots, ({\bf x}_n, y_n)\}$ where ${\bf x}_i \in \mathbb{R}^d$ and $y_i \in \mathbb{R}$.
Can we efficiently ...
- 12.7k
1
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0
answers
14
views
Tracking approximate values of specific percentiles
At the moment I use HdrHistogram to track approximate distribution of a stream of values. But I don't really need all percentiles, just three of them. Is there some algorithm to track specific ...
- 111
1
vote
0
answers
93
views
Differential Privacy with only positive noise
The Laplace mechanism is a standard way of making the output of a function $f$ differentially private.
More concretely, let $\Delta_f$ be the sensitivity of $f$, i.e. the maximum value by which the ...
- 269
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1
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53
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How to implement conditional probability distribution on set-valued Random Variables
I'm trying to implement conditional probability distribution when the events of two RVs are sets. If I try to extrapolate concepts from real or categorical variables to sets things become confusing ...
- 1
2
votes
1
answer
40
views
Averaging a list of variances
In a setting where I have n clients each owns a subset of the dataset, each computes the mean and variance on his data and send them to the server. The server would average all means and variances. ...
2
votes
1
answer
57
views
Is this statistical group summation unambiguously reversible?
Let $X$ be a finite multisubset of $\mathbb{N}^2$. Let's introduce the following notation:
$A$ is a set of all first elements of pairs from $X$ and $B$ is a set of all second elements of pairs from $X$...
- 247
2
votes
0
answers
25
views
Algorithm to mapping given probabilities to empirical probabilities
Consider following problem statement:
You have given $n$ actions. You can perform any of them. Each action gives you success with some probability. The challenge is to perform given finite number of ...
- 235
1
vote
2
answers
157
views
Find the average number of steps to sort an array by randomly selecting two elements
I have sequence of an unique numbers from 1 to 10 in randomly order (for example: list = [7, 5, 3, 4, 2, 6, 10, 1, 9, 8]). I can choose two random number and if the list from left number larger then ...
- 11
1
vote
1
answer
22
views
SGD statistical guarantee
I have a question regard online learning with SGD. Is there a way to give a statistical guarantee that the value obtained after $n$ samples deviates at most $\epsilon$ from the real value?
Thank you ...
- 117
0
votes
0
answers
34
views
How to handle distribution of values with same attributes into different classes
I'm a student studying a data mining course and have come across a problem.
I need to explain the problem with the help of an example scenario as I do not know how to explain the problem in any other ...
- 153
1
vote
1
answer
53
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Chebyshev inequality comparison
Given $n$ distinct values $(x_i)_{i=1}^{n}$ with mean $\mu$ and standard deviation $s$, for all $i$, we have $|x_i−\mu| ≤ s \sqrt{n − 1}$.
How does this inequality compare with Chebyshev inequality as ...
user126050
1
vote
1
answer
1k
views
Efficiently selecting a random subset of size $m$ from a set of size $n$
This is a cross post of my question here on math.se.
I have a list of $n$ items and would like to randomly select an $m$ set from it efficiently (in terms of time complexity). Also, I want all ...
- 189
2
votes
0
answers
55
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In a machine learning system, why use differentially private SGD if our input data is already perturbed by a DP mechanism?
I'm trying to implement my own version of a deep neural network with differential privacy to preserve the privacy of the parties involved in the training dataset.
I'm using the method by Abadi et al. ...
- 121
0
votes
1
answer
46
views
Gaussian distribution with condition?
What does this expression mean?
Normal distribution with condition
I am reading a research paper and found the following expression (Eq.28 in the paper below).
It means a Gaussian distribution, but ...
- 3
1
vote
2
answers
76
views
Algorithm for Estimating Number of Unique Monthly Visitors
Is there a way to estimate the number of unique monthly visitors to a site based on a limited sample of one week of data? I have information about when a given user visited the site. This isn't as ...
- 111
9
votes
1
answer
4k
views
What is the optimal algorithm for playing the hangman word game?
Suppose we are playing the game hangman. My opponent and I both have access to the dictionary during the game. My opponent picks a word from the dictionary with knowledge of the algorithm which I will ...
1
vote
1
answer
40
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Minimizing Trimmed Distances
I'm trying to understand what is the minimum of the following function,
$$
f(\mu) = \frac{1}{n}\sum_{i=1}^n F\left(\frac{\pi(i)}{n}\right) (x_i - \mu )^2
$$
where $F$ is a step function that assign $...
- 37
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votes
0
answers
35
views
Does this problem have a formal name?
I have come across the following problem but am unable to understand the solution for it. Hence I would like to know if it has a formal name then, I can search for it and read about it in more detail. ...
- 215
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votes
0
answers
79
views
How to find clusters of a set of points in n-dimensional space that are furthest from unwanted points
I have a list of 25 points and their coordinates in a 512-dimensional space. I have 8 target points and 17 points I need to avoid (the 17 points to avoid also have differences in priority of how ...
1
vote
1
answer
421
views
Amount of expected loop iterations when searching an array by random index
Lets say we have an array A of size n. It has 1 as its first index and n as its last index. It contains a value x, with x occurring k times in A where 1<=k<=n
If we have a search algorithm like ...
- 13