# Tag Info

Accepted

### FIR Filter Design: Window vs Parks McClellan and Least Squares

I agree that the windowing filter design method is not one of the most important design methods anymore, and it might indeed be the case that it is overrepresented in traditional textbooks, probably ...
• 80.4k
Accepted

• 41.3k

### Solving LASSO (${L}_{1}$ Regularized Least Squares) with Gradient Descent

It can easily solved by the Gradient Descent Framework with one adjustment in order to take care of the ${L}_{1}$ norm term. Since the ${L}_{1}$ norm isn't smooth you need to use the concept of ...
• 41.3k
Accepted

### Sequential Form of the Least Squares Estimator for Linear Least Squares Model

Slope from all samples obtained To summarize the question's problem, you want to calculate the slope based on all samples obtained thus far, and as new samples are obtained, update the slope without ...
• 12.5k
Accepted

### Questions on the Generalized Tikhonov Regularization

One way to interpret the Tikhonov Regularization is using the Maximum A Posteriori (MAP) framework. Lets' say we have a model of the form: $$\boldsymbol{y} = H \boldsymbol{x} + \boldsymbol{n}$$ ...
• 41.3k
Accepted

### Least Angle Regression (LARS) without Matrix Inversion

If you want to solve for single value of $\lambda$ in the model: $$\arg \min_{x} \frac{1}{2} {\left\| A x - b \right\|}_{2}^{2} + \lambda {\left\| x \right\|}_{1}$$ Then you can use Coordinate ...
• 41.3k

### Looking for the Concept About All In One Curve Fitting

You can always augment the matrices to do so. Let's assume the first model is given by: $${y}_{1} = {H}_{1} * {\theta}_{1}$$ The second model is given by: $${y}_{2} = {H}_{2} * {\theta}_{2}$$ ...
• 41.3k
Accepted

### What is the Concept of MATLAB Function Polynomial Interpolation?

It is basically an approach choice. Inside the math is identical. Usually, when doing Least Squares curve fitting, you're not looking for the Polynomial coefficients but a scaled version of them. For ...
• 41.3k

### Least Mean Squares (LMS) Filter Weight Update

That really depends on context, but generally adaptive implies that the calculations are done on-line / on the fly. In some applications, the filter is updated for a while, then the adaptation is ...
• 22.9k

### Least Squares with Non Zero Mean Noise

Since this is a linear model if you add noise which isn't centered (Non zero mean noise) your estimation will be good up to a bias term. The easy way to do so is to remove the bias from $y$ and ...
• 41.3k

### Least Mean Squares (LMS) Filter Weight Update

To expand on what Peter K. has said, if the signals being used by the filter are stationary, then the filter weights or coefficients can be determined and the filter operates as it was designed ...
• 414

### What Is the Difference between RLS, LMS and Wiener Filter? When Is One Preferred Over Another?

All three are Estimators / Predictors. All of them try to estimate the coefficients of Linear Filter which minimizes an MMSE Cost Function. The Wiener filter assumes all data is given and sets the ...
• 41.3k

### Python: Least Squares Support Vector Machine (LS-SVM)

There is a package called FukuML. In their description (Version 0.4.1) they write: Support Vector Machine Primal Hard Margin Support Vector Machine Binary Classification Learning Algorithm Dual ...
• 41.3k
Accepted

### Why Is Non Linear Least Squares Method from MATLAB and Alglib Gives Different Results on the Same Data?

When you solve Non Linear Least Squares problem of a non convex cost function the end solution (Which is guaranteed to be a Local Minimum) will depend on: Method of Minimization. Method Parameters. ...
• 41.3k

### Sequential Form of the Least Squares Estimator for Linear Least Squares Model

There are really great answers. I will try to give the Sequential Least Squares approach which generalizes to any Linear Model. Sequential Least Squares Model We're after solving the Linear Least ...
• 41.3k
Accepted

• 41.3k

### Zero Phase Filter: Determining Initial Conditions for Forward Backward Filtering

For anyone who is interested, i coincidentally found a paper describing the method implemented in matlab's filtfilt.m. A link to the paper is attached. At least to my understanding matlab's filtfilt.m ...
• 367