# Tagged Questions

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### How do I measure the goodness of cosine similarity scores across different vector spaces?

I am a computer scientist working on a problem that requires some statistical measures, though (not being very well versed in statistics) I am not quite sure what statistics to use. Overview: I ...
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### Choosing between increasing sample size and testing for failures

I have a large set of data that shows things (let's call them cars) have performed over the years against various different tests (say, crash test, braking, gas mileage, etc.). What I'm doing is ...
65 views

### Avoid dividing by zero with just variables and basic operators

I am working on stats for a sports team, and one of the stats I have the ratio of Shots and Shots on Target (Which I call ...
17 views

### Ranking Best Deck

I'm creating a ranking system for a set of decks. Each decks have different win rates and number of games. The decks are currently ranked by the win rate, but this isn't accurate at all since some ...
25 views

### How do you express the maximization step of EM algorithm in matrix formulation?

Specifically, I am interested in how the covariance matrix is calculated. In terms of dimensions of factors involved, let's say I am given some data set X of dimension m x d, covariance matrix S of ...
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### Why is Expectation Maximization algorithm guaranteed to converge to minimum, even local?

I have read a couple of explanations of EM algorithm (e.g. from Bishop's Pattern Recognition and Machine Learning and from Roger and Gerolami First Course on Machine Learning). The derivation of EM is ...
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### Wilson score for a range of ratings?

(Note: I did look at similarly worded questions and none seem to answer this one.) Given this scenario: People can rate 0 or more items on a scale of 0-X. I am trying to find the Wilson score ...
41 views

### Best way to generalize a distribution of data into smaller subsets?

Suppose I had a data set as follows: 168.95, 176.83, 178.13, 179.61, 179.44, 172.83, 173.37, 174.06, 174.94, 175.43, 175.73, 175.5, 173.78, 174.06, 172.71, 174.3, 178.38, 178.43, 177.18, 175.34, ...
66 views

### Ranking System (ELO)

I want to create a ranking system for a sports game, where more that 2 "teams/players" participate in each match. This means NOT chess, or soccer, or boxing. It could be bowling or long jump etc. For ...
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### algorithm for generating interesting normal symmetric continuous functions

Does any one know of, or can think of an algorithm which generates arbitrarily many symmetric normally distributed continuous functions? And when I say interesting I mean more complex distributions ...
33 views

### How to write this conversion algorithm

I have to calculate Grade Average from the scale of 1 to 5 such that 1 being the best (100%) and 5 being the worst (0%). So we have, ...
111 views

### Are there algorithms for generating aesthetically pleasing scatter plots?

I'm tinkering around with making a bokeh generator. Currently, all the positions are random, but the results are not often visually pleasing. It seems that what looks good is having around 3 ...
61 views

### K Nearest Neighbors classification Special Case with Identical Points

The question is about KNN algorithm for classification - the class labels of training samples are discrete. Suppose that the training set has n points that are ...
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### How can I find a villain's hideout given a set of previous locations? (Or, how can I identify the centeroid of a cluster of datapoints?)

Imagine this... Batman has just retrieved a tracking device he placed on The Joker 150 days ago. The good news is that it has 150 coordinates — one from each day. The bad news is that all the data ...
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### Some doubts related to statistic entropy concept in ID3 machine learning algorithm

I am studying the statistic entropy concept used by ID3 machine learning algorithm For a domain exemplified by the learning set S (that is the set of the examples that I use to build a decision ...
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### The relationship between fisher information and EM algorithm?

I wonder what is the relationship between fisher information and EM algorithm? When I read papers about EM algorithm, people sometimes discussed about fisher information, and there are algorithms ...
32 views

### Salesmen working time allocation

I was asked to solve the following problem: I'm given a big number of organizations org to call the next months m, having each of these a different working hours orgStartTime and orgEndTime and ...
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### Kernel distribution estimation

Due to an assignment I need to implement a algorithm based on KDE to schedule an input data in different servers. So far, I studied statistics in my bachelor but we did not go that far and they did ...
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### How to compute conditional expectation of a log function

I've been studying the Expectation Maximization algorithm. According to the formula shown here, what I have to do in the M step is to compute a new $\theta$ that maximizes the conditional expectation ...
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### Little hardcore: Do you know any parallel modified moving average algorithm?

Do you know any parallel modified moving average algorithm? I want quickly calculate moving average but not with sequential algorithms. I want to use parallel algorithms but I have still not found ...
154 views

### Quicksort analysis problem

This is a problem from a probability textbook, not a CS one, if you are curious. Since I'm too lazy to retype the $\LaTeX$ I will post an ugly stitched screenshot: This seems ridiculously hard to ...
195 views

### Simple random sample without replacement

I have a data file from which I wish to create a uniformly distributed simple random sample, without replacement. Will the following algorithm give me an unbiased result? ...
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### Statistical significance test in polygaussian fitting, using Levenberg-Marquardt

I have a set of dihedral angle values that I have fitted using a polygaussian function via the Levenberg-Marquardt algorithm http://en.wikipedia.org/wiki/Levenberg-Marquardt. Specifically, the ...
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### How to measure the streakedness of numerical data?

Would anyone know how to use C/C++ to calculate the streakedness of data? The definition of streakedness is how many deviations away from the mean(i.e running average a numerical data streak. Thank ...
118 views

### Effective model for calculating momentum or growth rate for a time series

I have a series of numbers tracking the performance of an entity on any given day. It's nothing but a simple integer for each date. For example, here's a series for Entity "X" ...
219 views

### 1/f “Pink Noise” for the Math-Disabled

I have very little skill when it comes to math beyond all the elementary level operations (addition, subtraction, multiplication, division, mean, mode, etc) and a vague grasp of statistics, what a ...
53 views

### Find factor of sample elements given the median

I have a sample $S(x)$ containing $n$ elements: $$S(x)=\{ s_1 x, s_2 x, \ldots, s_n x \},\qquad s_i \in \mathbb{R}, x\in \mathbb{R^{+}}$$ Every element in the sample is multiplied by $x$. Now ...
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### Statistic: calculating error of order of two sequences of objects

I am trying to derive a meaningful statistic from a survey where I have asked the person taking the survey to put objects in a certain order. The order the person puts the objects is compared to a ...
178 views

### Html Tag counting - Rate of Change formula

I've been trying to a find a statistics-esque formula for calculating the rate of change for html tags which are either added or removed from various websites. So, for example, with the scraper I'm ...
404 views

### Calculating Percentile Rank Using Relative Strength Ranking

I have a spreadsheet of stock quotes that contains Relative Strength Ranking (RSR) ranging from -45 to 65 and the count of ranks is 1500. Could someone please explain how I can calculate percentile ...
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### Finding an accurate rating between 1 and 10 based on numerous data points

I'm going to provide a fictitious setup that aligns with my mathematical needs. I am a company that is measuring the bounciness of balls and providing two 1-10 rating to each ball based on how it ...
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### How to transform normally distributed random sequence N(0,1) to uniformly distributed U(0,1)?

Everybody knows how to convert U(0,1) to N(0,1). However does anybody know an efficient algorithm solving the opposite task? I mean how to generate U(0,1) sequence from N(0,1) one? Asking because a ...
109 views

### Ranking System and Separated Populations

I'm trying to modify the ELO ranking system formulas to adapt them to eSport (electronic sports, but more specifically Starcraft II). (The reason I'm using ELO, is the straight forward concept and ...
130 views

### Working out the “best” score based on quantity and ratio

I'm not an expert with mathematics so I hope I'm posting in the right place! I've got a lot of products which can be rated good, bad and OK by a user. What I'm having trouble with is finding which is ...
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### Trying to create an algorithm that takes into account multiple variables

I've hit a road block on how I can put what I have into a calculation that works. Simply I am trying to work out the "value" of each company that we have on my companies books. The information I want ...
118 views

### MDS and low distortion embeddings

While googling about low distortion embeddings, I feel that there are two separate communities working on the subject of low distortion embedding, without much communication with each other. In ...
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### How can we find a new sum of multiplications based on a previous one?

Suppose wehave two sequences: $$(a_0, a_1, a_2, \dots, a_{2^n-1})$$ $$(b_0, b_1, b_2, \dots, b_{2^n-1})$$ We also have the following sum: $$\sum_{k=0}^{2^n-1}{a_k \cdot b_k}$$ I'd like to know the ...
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### Algorithm to predict next 3D points

For example, having this data: year x/y/z 2007 10/20/70 2008 20/10/70 2009 30/10/60 2010 40/10/50 2011 40/15/45 We want to predict what will be the x/y/z in ...
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### Prediction based on different factors

I have a problem bugging me for some time. I am developing a game and need to calculate the percentage of the capacity of a stadium that will be filled in relation with some factors: other team ...
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I have limited access to a collection $X_1,\ldots,X_m$ of sets of positive integers. Each $X_i$ is "moderately large" (a brief survey has found them to contain about $10^6$ elements in each set), but ...
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### Design an $O(n)$ deterministic algorithm to find the approximate median of an array

We have an unordered sequence $A$ which consists of $n$ different numbers $A[1],A[2],A[3],\dots, A[n]$. One member of $A$ is named an approximate median if $A$ contains at least $n/4$ members ...
154 views

### How does the backward/forward algorithm work if there is no end?

I'm using Jason Eisner's spreadsheet to understand HMM more better. There's a box at the top that have a transition matrix. I see the Cold day and Hot day options, but don't understand why there's a ...
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### Unbiased (random?) selection algorithm

Let say we have the following set $S = \{x_1, x_2, x_3, ..., x_n\}$ where $x_i$ is a real number between $0$ and $1$. Now I want to find an algorithm that randomly generates a subset of $S$, free to ...
464 views

### Boxcar Recursive Method for Finding Standard Deviation

I'm trying to develop a real time algorithm for finding level areas of an electrical signal. To do so I need to find the variance for a particular rolling time interval. From John Cook's blog and ...
73 views

### First hitting time for generalized Pólya urn

I have looked around the literature but I've not found a clean answer to the following. Imagine that you have a generalized Pólya urn (GPU) in the sense of Pemantle's survey (Section 2.1 in ...
588 views

### Velocity Measurement Error Estimate

I have 2 position estimates (along with their measurement error) and a difference in time between estimates. I estimate velocity using ...
157 views

### calculate the rate of change

I am trying to calculate the change frequency for a set of data. Each bit of data has the date-time it was created. I would like to say for a specific set of data the change frequency is hourly, ...
162 views

### Formula to generate a score from 1 to 100 based on 2 percentages?

I am trying to come up with a formula that will result in a score of 1 to 100 (never anything lower or higher). I have two numbers that I can use to come up with this score, a specific percent and an ...