Questions tagged [statistics]

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55 views

Infer probabilities, for concatenation of words

Fix an alphabet $\Sigma$, and a set of words, $W = \{w_1,\dots,w_n\} \subseteq \Sigma^*$. I have a randomized model that works like this: Alice generates a random sequence of words, using some ...
4
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0answers
300 views

Space complexity of statistic functions

When computing statistics on a list of data it occurred to me that most of the standard statistic functions, such as mean, min, max can be computed in O(N) time with O(1) space. They can also be ...
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81 views

Statistical anomaly detection in time series

I'm looking for some algorithms that detect statistical anomaly in time series. For example, Google Trend automatically detects peaks of a specific search query in time, and associates those peaks ...
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0answers
20 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 ...
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0answers
23 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 ...
2
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0answers
44 views

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. ...
2
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0answers
38 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 ...
2
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0answers
28 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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0answers
100 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 ...
2
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0answers
115 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 ...
2
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0answers
35 views

error measure (of ML agos) that takes confidence into account

when calculating the error measure such as mean absolute error, we use the real values and the predicted values. Many machine learning algorithms can give a confidence measure of each value being ...
2
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0answers
45 views

Do online quantile estimation algorithms that support deletions exist?

There are several online quantile estimation algorithms, but I haven't seen any that supports deletions (i.e. unobserve elements observed in the past). Are there any such known algorithms? To ...
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0answers
286 views

Efficiently estimating latency quantiles of a distributed system

I'm building a load test harness for a distributed system. Currently I'm using the "Cormode, Korn, Muthukrishnan, and Srivastava" method to estimate latency quantiles of system responses. I'm now ...
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11 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 ...
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15 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 $\epsilon$-...
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28 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} -...
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13 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 ...
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0answers
21 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 ...
1
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0answers
77 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
33 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 ...
1
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0answers
69 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 ...
1
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0answers
42 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,...
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0answers
34 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 ...
1
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0answers
79 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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238 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 ...
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0answers
57 views

Known distributions that generate sparse vectors?

I have data that comes in the form of a vector. Each vector is sparse. Is there a commonly used distribution that will generate sparse vectors? I am working on a project where I am passing a bunch ...
1
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0answers
245 views

Linear regression - iterative approach

I have a single output variable $y$ and a number of inputs $x_1$, $x_2$, etc. These are time series. Each $x_i$ explains the changes in $y$ in specific circumstances, and the goal is to have a linear ...
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0answers
189 views

Formula for number of parameters in an undirected graphical (probability) model

I have googled endlessly, and I cannot find it. Can anyone point me to a reference that gives a way to calculate the number of parameters in an undirected Graphical Model? Adapting from the similar ...
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0answers
94 views

Applications of algorithms to stock trading analysis

There is a new Quantitative Finance SE site. However, I am interested in asking the "CS crowd": What are some interesting key references or surveys on applying algorithms to stock trading analysis?...
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22 views

Simple Bayesian Question

I have the following Bayesian Network. I have worked out the following: P(H) = P(H|D) + P(H|¬D) = 0.5 + 0.1 = 0.6 P(D|H) = (D)∗(P(H|D) +P(H|¬D)) = 0.3∗(0.5 + 0.1) = 0.18 How do I compute the ...
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43 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) = ...
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1answer
88 views

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 ...
0
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1answer
38 views

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 ...
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0answers
16 views

what is instrument validation in computer science?

I'm writing an assignment involving some statistics comparing different implementation methods for web applications. I'll be using some downloaded software and web pages I create, on both virtualized ...
0
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1answer
80 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 ...
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0answers
27 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 ...
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0answers
32 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
45 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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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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53 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 ...
0
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1answer
76 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 ...
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0answers
43 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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0answers
30 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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0answers
74 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: \...
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0answers
151 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 ...
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0answers
58 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 ...
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0answers
392 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?
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0answers
222 views

Merging two disconnected graphs

Firstly, I'd like to apologize for any misused terms or ways I could have made the description much more succinct. It's been a while since I took machine learning during my bachelor's. I have two ...
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0answers
83 views

TF-IDF query engine in context of terms weight

I'm looking for public algorithm which gives the engine these abilities: Query by ranked terms Limit outcome by date/time range Basically, i'd like to concentrate articles (generally ...
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2answers
107 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 ...