Questions tagged [statistics]

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30 views

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 $...
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29 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. ...
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0answers
25 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 ...
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1answer
59 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 ...
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0answers
16 views

Kullback-Liebler Divergence

For $P(x)=N(\mu,\sigma^2)$ and $Q(x)=N(0,1)$ I am supposed to calculate $KL(P(x)||Q(x))$, here is what I did \begin{align*} KL(P(x)||Q(x)) & = \int P(x) \cdot \log\left(\frac{P(x)}{Q(x)}\...
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22 views

Difference between GA and ABC for inference

If I have an agent-based model and I want to infer the parameters, I would normally used ABC (approximate bayesian computation), but I was recently working with someone who was using GA (genetic ...
3
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1answer
156 views

Measures of performance in machine learning

I'm new to machine learning and struggle to interpret the results I get from different measures of performance. If for several prediction models I have e.g. accuracy, precision, recall, F1, FPR, and ...
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0answers
87 views

vc dimension of binary decision trees of depth d?

how do i find the vc dimension of the hypothesis space H ,of the binary decision trees of depth d-2? will the hypothesis space H consist of{0,1} and the vc dimension is the number of ways in which we ...
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0answers
41 views

Suggestion for a good statistics book for computer scientists, in preparation of machine learning

We (a group of CS postdocs and Ph.D. students) are starting a shared reading of a machine learning book ("An Introduction to Statistical Learning", James, Witten, Hastie, Tibshirani). Before diving ...
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0answers
28 views

The No-Free-Lunch Theorem and K-NN consistency

In computational learning, The NFL theorem states that there is no universal learner. For every learning algorithm , there is a distribution that causes the learner to output a hypotesis with a large ...
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0answers
27 views

What is the purpose of standardization in machine learning?

I'm just getting started with learning about K-nearest neighbor and am having a hard time understanding why standardization is required. Reading through, I came across a section saying When ...
2
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1answer
42 views

Estimation of the number of solutions by Counting

This is a question from a quantum computation textbook. Consider a classical algorithm for counting the number of solutions to a problem. The algorithm samples uniformly and independently $k$ times ...
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46 views

What kind of standard deviation must be used in optimization algorithms?

I would like to ask about the standard deviation of objective function value. There are two types of standard deviations: Population standard deviation Sample standard deviation In metaheuristic ...
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1answer
17 views

Assumption of a generation of the dataset by a probability distribution

Consider the following paragraph from the deeplearningbook The training and test data are generated by a probability distribution over datasets called the data-generating process. We typically ...
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1answer
64 views

How can we get small test error reducing only train error?

My question is about mathematical part of machine learning algorithms, especially about using it in neural networks. We train network reducing train error and I was thinking about how then test error ...
3
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3answers
94 views

How good (or bad) is my makeshift PRNG?

Say I have designed a makeshift PRNG for my personal amusement, now I would like to see how good it is. How do I benchmark its "randomness"? Ideally, I want to know a statistics test, such that if I ...
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0answers
23 views

How to go about designing a quiz that changes difficulty based on user performance?

I thought about using a machine learning algorithm to learn the performance patterns of the quiz taker and model the next quiz based on how he/she performed. So each question will have a difficulty ...
2
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2answers
46 views

identify abrupt frame changes in a video

The frames of live streams or videos, in general, do not flow smoothly. A sports game would have multiple cameras recording the game and hence, there will be camera switches in the stream. I am ...
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2answers
138 views

probability of collision

my data's range is from 1 to 9 and I have two subsets of integers from this range. the hash function takes each of this subsets and calculate product of these three integers and maps this set to the ...
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0answers
39 views

Optimize Algorithm For Shut in Box Game

This game is a simplified version of Shut the Box. There are 9 tiles (1,2,3,4,5...9). The initial tiles are unflipped. You have 2 dices. Each round, the player rolls the 2 dices and their sum is S. ...
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1answer
163 views

Is there a fast algorithm for computing the rolling mode of an array of integers?

I was wondering if there exists an efficient algorithm for calculating the "rolling mode of an array of integers. By rolling mode I mean that we have an array of integers of size $n$ and a sliding ...
2
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1answer
1k views

Median of two sorted arrays of different size in logarithmic time?

The solution given in Cormen is as follows: Reading this solution, the first doubt that comes in my mind is what if the median lies in array B. According to this solution, we are applying binary ...
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0answers
27 views

Locality sensitive hashing with non-scalal values

Locality sensitive hashing works well when matching is between vectors of scalars, but I now need to extend LSH to compare matrices. Each matrix is formed of n readings from m sensors forming a n by m ...
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1answer
36 views

How to find a possibility of match in Naive Bayes Classifier?

My math level is very very poor so I can't get the statistics. Can anyone explain in simple words? I.e. if I have frequency data: ...
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1answer
26 views

Testing two distributions, both accept null hypothesis

I have a sample that is collected to verify the accuracy of a new random number generator. Applying the goodness of fit test to check if this sample comes from the Standard Normal Distribution and ...
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0answers
88 views

Examples of bad statistics in Computer Science

I am preparing class materials for the applied statistics class for Ph.D. students and want to present them with examples of bad statistics in different fields of computer science. I am especially ...
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0answers
64 views

What is the reason behind getting same result by maximum likelihood estimate and smoothing?

I know that Good-Turing smoothing helps us to trim a bit of probability from some more frequent events and give it to the events we've never seen. Thus it keeps our model from assigning zero ...
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0answers
64 views

SimRank++ on a weighted graph (why the formula reflects the influncee of the weight)

In the paper "Simrank++:Query Rewriting through Link Analysis of the Click Graph"(http://www.vldb.org/pvldb/1/1453903.pdf), the formula to compute the similarity between $q$ and $q'$ is as follows: \...
1
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1answer
67 views

Inequality over the entropy of an integer-valued random variable

I stumbled upon this inequality over a course on Information Theory : If $Z\in\mathbb{N}​$ with finite mean, then $H(Z) \leq E(Z)\times h(\frac 1 {E(Z)})​$ where $h$ is the binary entropy function ...
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2answers
176 views

Applying graph “adjustment” algorithms to Elo rating system

I'm trying to address what I perceive to be a potential shortcoming in the Elo Rating System (predominantly used by the international Chess community to rate + rank players). I have a two-player game ...
0
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1answer
313 views

maximizing inner product of vectors in an ellipsoid and a given vector

I have been wrestling with this for quite a long time but couldn't convince myself that the following is true: What I do understand: $\theta_a$ denotes the set of points that are within the ellipsoid....
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0answers
40 views

Update model parameter with new data, discarding old data

I have this dataset, and I am using y = (a * x^n) / (b + x^n) Hill function as the model, where a is the limit of the Hill curve,...
3
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1answer
32 views

HMM tagger - Baum Welch training

I am trying to implement a trigram HMM tagger for a language that has over 1000 tags. In my training data I have 459 tags. Now if we consider that states of the HMM are all possible bigrams of tags, ...
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0answers
30 views

Unsupervised learning: necessity of labels and dependency between features and labels?

I have logs of activities without labels, which describe whether an activity is normal or not. Assuming that normal behaviors will follow a Gaussian distribution, I fit Gaussian distributions on ...
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2answers
314 views

Trying to Classify MNIST where pixels are shuffled with a seed.Why is it not working?

I transformed the MNIST dataset as follows:(X (70000 x 784) is the training matrix) ...
0
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2answers
74 views

Estimating run time in the absence of knowledge

I’ve always wondered how to make a best guess in the absence of any knowledge. Let’s say you have a computation running, and you don’t know when it will complete (just that it will). Can you make any ...
2
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0answers
112 views

What would be the probabilty of a randomly generated tree to be a Red-Black Tree

The question is not related to the homework I was working on a homework, and the specification was to generate a random tree with n elements(n being in the thousands for the assignment) and asked me ...
1
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1answer
487 views

how to interpret the coefficients of binary logistic regression?

I'm working on a kNN classifier to classify whether a text is written by a man or a woman on the basis of the most frequent words. However, a kNN doesn't show which features were the most important in ...
1
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2answers
43 views

If we can $\epsilon-$cover one set with $\frac{K}{2}$ elements and another with 2 elements why isn't their set product $2^{\frac{K}{2}}$ cover?

I was reading the following paper on Robustness and Generalization (and covering numbers)and I was reading their example 1: which didn't quite make sense to me. The reason it didn't make sense is ...
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0answers
117 views

“Sensitivity” of algorithms

Let us assume that we have two algorithms, $A$ and $B$. Based on 3 different values of a parameter, $P$, $A$ takes $a_1, a_2, a_3$ seconds and $B$ takes $b_1, b_2, b_3$ seconds. What would be a proper ...
1
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1answer
35 views

What is the theory behind testing fixes for intermittent bugs?

I ask this question because I deal with alot of intermittent bugs and want to be able to answer the question "Can I be at least 95% sure that my changes to the code fix the bug?". I've got some ideas ...
0
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1answer
48 views

How to find a good saw function for PRNG?

As part of an assignment I have to write a PRNG using a sin (or any other trigonometric function) and a saw function which I'm struggling a bit with. So how would you find a good saw function with ...
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2answers
94 views

finding normality from a set of samples of MEAN

I have set of 1000 samples. each sample represents MEAN of X amount transactions response time. Now I have a running transaction , I know it's current response time but I want to know if this ...
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0answers
50 views

What is the probability distribution of arrival times in a distributed system?

I'm going to simulate an asynchronous distributed system. In a distributed system, when a node sends a message, after $\Delta t$ seconds the message reaches to its destination. My Question: What is ...
4
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1answer
4k views

Showing that Bayes classifier is optimal

Consider domain $X$, label set $ Y=\{0,1\}$ and the zero-one loss. Given any probability distribution D over $ X\times \{0,1\} $, we've defined the Bayes classifier $ f_D $ to be- $$ f_{D}(x)= \...
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0answers
64 views

Approximate conditional entropy

Given a set of random variables $X = \{x_1, x_2, \dots, x_n\}$. If the conditional entropy for all $Y \subset X - \{X_i\}$ where $|Y| \leq 5$. How to approximate conditional entropy when $|Y| = 10$ ...
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0answers
228 views

EM-algorithm for categorical hidden variables

I have the following model: Let's say two indepentent weighted six-sided dice $X$ and $Y$ with unknown probabilities (i.e. probability of 1 is unkown etc) and they have not necessarily the same ...
6
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2answers
175 views

How best to statistically verify random numbers?

Lets say I have 1000 bytes that are supposedly random. I want to verify to a certain certainty that they are indeed random and evenly distributed across all byte values. Aside from calculating the ...
3
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2answers
120 views

Redistributing a set of uniformly distributed numbers to an arbitrarily defined shape

Lets say I have a random number generator that spits out uniform numbers from 0 to 1 Next, I have a shape defined by a series of vertices, like { [0, 0.4], [0.5, 0.2], [1, 0.4] } In those vertices, ...
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0answers
377 views

What is role of parameter learning rate, lr, and momentum constant, mc in Neural Networks?

can anyone describes the more simplified mathematical formulation of learning rate, lr, and momentum constant, mc in Neural Networks while training the data?