Questions tagged [algorithms]
An unambiguous list of computational steps involved in finding a solution to a class of problems.
945 questions
0
votes
0
answers
39
views
Efficient algorithm to approximately sample from random walk
Let $X_0,X_1,X_2,\dots$ be the simple random walk, i.e., $X_0=0$ and each $X_{t+1}$ is sampled uniformly at random from $X_t-1,X_t+1$ independently of everything else.
Given a very large $t$, I want ...
- 7,188
14
votes
2
answers
441
views
How can I estimate a function from its level sets?
I am developing an app. Let $f:X\subseteq \mathbb{R}^n \rightarrow \mathbb{R}$ be a function satisfying some regularity conditions (e.g. continuity and smoothness), and let $2 \leq n \leq 100$.
$f$ ...
- 404
0
votes
0
answers
66
views
What does iteration in sigma clipping do
If I only want the high-SNR data, I do sigma-clipping to an array.
As this link says
Suppose you have a set of data. Compute its median m and its standard deviation ...
4
votes
1
answer
89
views
Stochastic Gradient Descent for Multilayer Networks
I was going through the algorithm for Stochastic Gradient decent in mulilayer network from the book Machine Learning by Tom Mitchell, and it shows the formulae for weight update rule. However, I dont ...
- 49
3
votes
1
answer
125
views
Incorporating extra data from one sample when comparing 2 distributions?
Given that I have 3 samples $X_1^{(1)},\dots,X_n^{(1)}\sim P_X$, $X_1^{(2)},\dots,X_n^{(2)}\sim P_X$, and $Y_1,\dots,Y_n\sim P_Y$ -- let us assume that $P_X$ is different from $P_Y$. I would like to ...
- 355
0
votes
1
answer
132
views
Comparison of Two Algorithms for Finding a Position of 1 in an Array with Equal Zeros and Ones
Given an array 𝑎[1..𝑛] containing half zeros and half ones, we need to find a position in 𝑎 that contains the value 1. Consider the following two algorithms:
Algorithm 1
...
1
vote
0
answers
62
views
Do weights update less towards the start of a neural network?
That is, because the error is coming from the end of the neural network (ie at the output layer) and trickles back via backpropagation to the start of the neural network, does that mean that the ...
- 11
0
votes
0
answers
73
views
Optimizing $\alpha$ parameter in $\alpha$-shape calculations: to what precision?
I am calculating alpha shapes for a large amount of 3D point clouds (each of ca 2000 pts). They are fairly homogeneous and has a sphere-like topology while concave, but of course contain some finer ...
- 143
3
votes
2
answers
196
views
What is the difference between an algorithm and a model in statistics and data analysis?
A student asked me, "What is the difference between a model and an algorithm?"
I explained the difference between a model and an algorithm as follows.
In my opinion, a model is a ...
- 1,359
0
votes
0
answers
86
views
Custom algorithm to create a normal distribution from a uniform distribution, struggle with a parameter
I made a custom algorithm to convert a uniform distribution to a random distribution, but struggle with a parameter.
Here is the code in R:
(I'll explain the main idea and the parameters)
...
1
vote
0
answers
33
views
Efficient way to compute RBF kernel matrix after linear transformation
I have a dataset of points $\{\mathbf{x}_i | \mathbf{x}_i \in \mathbb{R}^n\}$ and a linear transformation matrix $\mathbf{F} \in \mathbb{R}^{n \times m}$, such that $\mathbf{y}_i = \mathbf{F}^T \...
- 2,362
3
votes
0
answers
76
views
Reservoir sampling vs Sampling excluding replacements
I am trying to understand the tradeoff between using Reservoir sampling Algorithm L and generating random values until I have enough unique values. This separates into finding the expected value for ...
- 81
1
vote
1
answer
100
views
No Free Lunch (NFL) theorem and average performance over all training sets of a given size N of a specific data generating distribution
I am trying to delve a little bit deeper into the implications of the No Free Lunch (NFL) theorem for supervised learning. The basic form of NFL is that averaged all data generating distributions all ...
- 881
1
vote
0
answers
53
views
Spatial Temporal Clustering evenly spaced over time
I have a large dataset of spatio-temporal data. It has longitude and latitude coordinates, and a date for each observation. For example:
Long
Lat
Date
50
20.43
9-19-2010
51
19.5
10-4-2010
51
19.3
10-2-...
- 143
1
vote
0
answers
22
views
Ask a coding problem for the equivalence of unconstrained Optimization with L1 Regularization [duplicate]
I recently read a statistics paper. It has an unconstrained problem:
$$\min_\theta F(\theta)+\lambda || \theta||_1$$, where $$F(\theta)=L(\theta)+\frac{\rho}{2}|h(W(\theta))|^2+ \alpha h(W(\theta))$$
$...
- 21