# 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 ...
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### 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 ...
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 ...
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 ...
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 ...
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. ...
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 ...
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 ...
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 ...
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### 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 ...
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 ...
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 ...
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 ...
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 ...
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 $\epsilon$-...
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} -...
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 ...
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 ...
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 ...
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 ...
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 ...
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,...
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 ...
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 $|Y| = 10$ ...
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 ...
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 ...
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 ...
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 ...
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?...
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 ...
43 views

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### 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?
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 ...