3
votes
1answer
54 views

Minimum required data for cosine fit

With a minimum amount of (noisy) data-points, I need to find the amplitude of a simple cosine y=A*cos(x), where x is an angle from 0:2pi. I know how to fit data to the function, and I know how to ...
0
votes
0answers
51 views

Calculating the “likelihood of progressive fit”

I am faced with the following least squares model fitting problem: I have a process that generates time series data. This time-series data have a specific structure (i.e. i can fit a model with ...
0
votes
1answer
62 views

Jacobian in Levenberg-Marquardt for 4-Parameter equation

I am trying to fully understand how I can use Levenberg-Marquardt to minimise a 4 parameter equation. There are lots of fancy programs to do this but the documentation about the mathematics is ...
1
vote
1answer
110 views

Relationship between lagrange multiplier and constraint

I know there is one to one relationship between $\lambda$ and $t$ in the following two equivalent optimization formulation. But what is exact relationship? A) $$ \sum_i(y_i - \sum_k \beta_k ...
-3
votes
2answers
91 views

Guess the functional form of a graph

Can you guess the functional form of the following curve y is 0 at x= Infinite ; y is very small ( +ve near to zero) at x=0 Thanks and regards
2
votes
1answer
343 views

Lasso - constraint form equivalent to penalty form

We know that there are two definitions to describe lasso. Regression with constraint definition: $$\min\limits_{\beta} \|y-X\beta\|^2, \sum\limits_{p}|\beta_p|\leq t, \exists t $$ Regression with ...
1
vote
3answers
513 views

Exponential extrapolation

Given a set of points on 2D surface $(x_1,y_1),(x_2,y_2),\ldots,(x_n,y_n)$ and a function $f(x)=k+ab^x$, the task is to find values of $k,a$ and $b$ that minimize the following sum: $$\sum_{i=1}^n ...
3
votes
2answers
165 views

How many points to find a polynomial?

I would like to fit a formula $ax^b + cx^d+ e$ to a set of points. I have two questions. If my data were perfect, how many points do I need in the worst case to get $a,b,c,d,e$ exactly? If my data ...
2
votes
2answers
182 views

maximize log determinant subject to a linear constraint

Does anyone know any efficient method to solve the following problem? $ (\alpha,\beta) = \text{argmax} \log \det (\alpha K_1 + \beta K_2)$ s.t. $c_1 \alpha + c_2 \beta = c_3, \alpha\geq0, \beta\geq ...
0
votes
1answer
51 views

How to find optimal border that defines, who is “friend”

I have the data about usage of several services in the population and the data about interactions among users. The idea is to determine, who is user's friend and who has interacted just ...
0
votes
1answer
28 views

Optimization, solving for the 'error' coefficient

Given a modified regression equation: $\hat Y = \exp(\beta_0 + \sum\beta_ix_i + \varepsilon)*F$ where: $\hat Y = 11353$ $\beta_0 = 8.693021$ $\sum\beta_ix_i = 5.95487177696$ $F = 0.21829$ what ...
1
vote
0answers
96 views

Jacobian approximation at given point without explicit derivatives expression

after solving a NLproblem with optimization method, I would like to compute confidence intervals, prediction bounds and standard deviation for these optimal parameters. Explicit formulas I have read ...
0
votes
0answers
146 views

How to find the best (integer) polynomial equation?

This is a continuation of How to find curve equation from data? I asked earlier. I am looking for both a formula and the method to find the best (integer) polynomial that fits my data. I still ...
1
vote
0answers
354 views

Moore–Penrose pseudoinverse reference

Given the eigendecompositions $AA^{\top}=Q \Lambda Q^{\top}$ and $A^{\top}A=P \Lambda P^{\top}$, where $\Lambda$ is a diagonal matrix (of eigenvalues) and $P$ and $Q$ are unitary eigenvectors matrices ...
3
votes
0answers
232 views

Least Square Method with Positive Parameters

this is my first post here in the Stack Exchange. A friend told me about this forum and I'm giving it a try. I searched a bit past threads, but couldn't find what I wanted, so I'm posting the problem ...
1
vote
1answer
658 views

Simple non linear fitting question(Least Squares Fitting--Exponential) [duplicate]

Possible Duplicate: easy to implement method to fit a power function (regression) I have the following simple function: $h = cV^n$ h and V being the variables and $c$ and $n$ are ...
0
votes
1answer
110 views

Getting linear regression of huge numbers

I'm trying to get a linear regression slope and intercept for a large set of huge numbers. I'm doing this on a computer, but I keep getting overflow errors (attempting to calculate a number too large ...
1
vote
0answers
217 views

Point-wise error estimate in polynomial regression

In our application we wish to estimate the actual path of objects. We have a set of samples of object locations $(t_i, x_i, y_i, P_i)$ where $t_i$ is the sample time, $(x_i, y_i)$ is the 2D location, ...
2
votes
0answers
62 views

Accurate computation for Linear Regression case

I am writing a program that inputs a sequence of points $(x_i,y_i)$ based on the user clicking on certain pixels in an image shown. The program should then find the "best -fitting" line in the least ...
5
votes
2answers
2k views

Linear regression for minimizing the maximum of the residuals

We know that simple linear regression will do the following thing: Suppose there are $n$ data points $\{y_i,x_i\}$, where $i=1,2,\dots,n$. The goal is to find the equation of the straight line ...
10
votes
3answers
1k views

Best fit ellipsoid

Given a collection of points $P \subset \mathbb R^3$, a crude characterization of the "shape" of $P$ is sometimes given by the principal components. We construct a covariance matrix, e.g., if $P$ is ...