Questions tagged [parameter-estimation]
The parameter-estimation tag has no usage guidance.
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Is there anyway to evaluate the estimation results of least square
Consider the scenario where a practical problem is tackled utilizing the method of least squares. Upon each iteration, an estimation of the parameter $\theta$ is derived via $\hat{\theta} = (X^\top X)^...
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Optimizing decision tree
I have a question regarding the technique/technology which could be applied for the issue:
Suppose I have a rule-based tree or decision tree which predicts a variable Y based on variables A,B,C. This ...
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Is probabilities mean of predicted class (RandomForest) a consistent estimator of class recall?
I'm working on a classification problem in order to predict among 50 different classes.
I'm using a Random Forest classifier and I'm using the predict_proba method ...
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Depth Estimation Algorithms without Reference Image in Computer Vision for Webcam Captured Video Data of a Person
I am currently working on a computer vision project that involves analyzing video data of a person captured from a webcam. In this project, I need to compute the depth map or distance of a specific ...
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Learning additional parameters that are not weights of a neural network
In addition to training the weights of a neural network, I also want to optimize other parameters (that are constant but satisfy some conditions over the entire data set). As an example, one can ...
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Is number of Parameters a sufficient benchmark for measuring how much resource the end model will use?
I want to do a platform-free benchmark for some custom ML models. Calculating the elapsed time during making predictions from certain size data is not suitable since I am constantly using different ...
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Using scipy.minimize to find the maximum likelihood estimates for multivariate gaussian
Let's say I have a 100x2 normally distributed array of data.
...
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How are parameters selected in cross-validation?
Suppose I'm training a linear regression model using k-fold cross-validation. I'm training K times each time with a different training and test data set. So each time I train, I get different ...
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Verifying my understanding of MLE & Gradient Descent in Logistic Regression
Here is my understanding of the relation between MLE & Gradient Descent in Logistic Regression. Please correct me if I'm wrong:
1) MLE estimates optimal parameters by taking the partial derivative ...
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Why should MLE be considered in Logistic Regression when it cannot give a definite solution?
If MLE (Maximum Likelihood Estimation) cannot give a proper closed-form solution for the parameters in Logistic Regression, why is this method discussed so much? Why not just stick to Gradient Descent ...
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The fine line dividing ML modelling and statistical modelling
I've been thinking about the difference between ML modelling and statistical modelling.
I would to ask, on a philosophical level, is my thinking correct: modelling is basically a process of fitting a ...
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Is there any library to perform robust clustering given two probability distribution with noise?
Given a dataset $X$ consisted with $w|X|$ samples drawn from a mixture of multivariate Gaussian distributions (say in two dimensions) and $(1-w)|X|$ samples of noise, is there any ...
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Understanding the likelihood function
The likelihood function is defined as -->
P(Data|Parameter) - This means, "The probability that the parameter would generate the observed data". Here, data refers to the independent ...
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Building a Model for Time Series Data in R (no forecasting)
Problem: I had planned to use a linear regression model to model time series data in retrospect (i.e., no forecasting). However, I am wondering if this is the best option having come across a few ...
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What is the best way to model survival when the hazard rate decreases over time?
The standard survival analysis model - for example the model which forms the basis for the proportional hazards model - assumes the hazard rate is constant. In many applications this would be the ...
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predict parameters of linear function
My questions seems very trivial, but I can't quite grasp it. I am also aware this post asks for opinions and knowhow, but do not know were else to ask. I do have quite a lot of experience solving even ...
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MLE for Poisson conditioned on multivariate Gaussian?
I am writing some Python code to fit 2D Gaussians to fluorescent emitters on a dark background to determine the subpixel-resolution (x, y) position of the fluorescent emitter. The crude, pixel-...
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How to reverse engineer a logarithmic equation
I am trying to reverse engineer the parameters of a human-designed logarithmic equation. Here are the facts:
The equation is of the type a = x * ( y ^ b )
a and b are known, x and y are unknown and ...
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How to get the maximum likelihood estimate of the categorical distribution parameters using Lagrange optimization?
Let's say our data is discrete-valued and belongs to one of $K$ classes.
The underlying probability distribution is assumed to be a categorical/multinoulli distribution given as $p(\textbf{x}) = \...
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Books about statistical inference [closed]
I'm currently taking a course "Introduction to Machine Learning" which covers the following topics:
linear regression, overfitting, classification problems, parametric & non-parametric ...
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how to find the best parameters to solve a differential equation? [closed]
I have a differential equation:
def func(Y, t, r, p, K, alpha):
return r * (Y ** p) * (1 - (Y / K) ** alpha)
and I want to find the best parameters that fit (r,...
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Estimate class proportions of a feature, central limit theorem
haven't been feeling smart lately and this is probably the most trivial question ever but I really need to know. I'm trying to point estimate some population parameters. I sampled from 1000 randomly ...
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Correcting high AR(1) coefficients in dynamic Gordon model
I have just finished my thesis on a heterogeneous dividend expectations model applied to the COVID-19 crisis! However after receiving some feedback there is one last issue I want to resolve. I'm using ...
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How should rolling window of parameter estimates look like?
I am using Orstein-Uhlenbeck model to model inflation: $dI_t=\theta(\mu-I_t)dt+\sigma dW_t$.
I have plotted rolling window estimates of all the parameters. However, I do not understand what to ...
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Pearson correlation coefficient - is correlation estimator acceptable?
As far as I know when it comes to theory, we use Pearson correlation when we want to check the correlation between two variables, which are both continuous or discrete. For a mixed case it's not so ...
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Why Maximum Likelihood Estimation for normal distribution?
Since we can compute the mean and the standard deviation of a set of random variables, why do we use Maximum Likelihood Estimation to estimate these parameters?
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Why Huber loss has its form?
Huber loss formula is
$\hspace{3.0cm} L_\delta(a) = \begin{cases} \frac{1}{2} a^2 && |a| \leq \delta \\ \delta (|a| - \frac{1}{2} \delta) && |a| > \delta\end{cases}$ where $a = y - ...
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Mapping 4 Dimensional array to predicted output text
Iv been studying machine learning but im struggling with some concepts and cant seem to find particular answers to the question of how theoretical data is mapped into non classification categories.
...
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Paramaeter estimation in noisy conditions with Machine Learning, possible?
Let's take two constants, $\alpha$ and $\beta$, both are given by two functions $f_1(\vec{\theta})$ and $f_2(\vec\theta$) (the model). These functions are known: we have an analytical closed ...
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Can Expectation Maximization estimate truth and confusion matrix from multiple noisy sources?
Suppose we have $m$ sources, each of which noisily observe the same set of $n$ independent events from the outcome set $\{A,B,C\}$. Each source has a confusion matrix, for example for source $i$:
$$...
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Maximum likelihood estimation vs calculating distribution parameters "manually"
I'm sorry for asking probably elementary question, but I cannot understand how estimating probability distribution parameters using maximum likelihood estimation method differs from calculating these ...
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Should I fit my parameters with brute force
I am running analysis on data for this type of sensor my company makes. I want to quantify the health of the sensor based on three features using the following formula:
sensor health index = feature1 ...
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Number of events estimation
I have three different histograms (Impact parameter distributions) corresponding to three groups of the same particle with different properties. However, the three distribution have more or less the ...
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How to calculate ideal Decision Tree depth without overfitting?
What would be a good way to go around finding the best depth for a DecisionTree (in SKLearn)? How can I tell if I've gone too deep and am overfitting? I know I can find the best parameters with f.e. ...
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Parameterization regression of rotation angle
Let's say I have a top-down picture of an arrow, and I want to predict the angle this arrow makes. This would be between $0$ and $360$ degrees, or between $0$ and $2\pi$. The problem is that this ...
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What is "oracle" in statistics?
When I read several statistical papers, they mention "oracle" property or "oracle" estimator.
What do they mean by "oracle"?
I understand this oracle is not a company name, but have no idea what this ...
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Parameter estimation for a model with multiple input parameters
So I've this model that simulates an ecosystem and outputs its attributes, like its chemistry, temperature etc. There are lots of input parameters to the model.
My job is to write a program to figure ...
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Lasso implementation in Python
I am working on this course on Machine Learning 2012 from UBC (CPSC 340). I am stuck on a Homework code problem which shows the following RuntimeError in ...
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How does one fine-tune parameters and weights at the same time?
I have been having my hands full with training a model to classify web pages. This is the first time ever that I am doing this, so I know very little about ML. I'm here to learn. ...
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Finding parameters of image filter using classified pairs
I want to solve the problem of finding a parameter vector for an image filter (let us assume we know nothing about how the filter works, but we can feed it an input image and a set of parameters to ...
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CNN memory consumption
I'd like to be able to estimate whether a proposed model is small enough to be trained on a GPU with a given amount of memory
If I have a simple CNN architecture like this:
...
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How do I choose the optimal parameters for reliefF
For feature selection I use reliefF provided by matlab.
The reliefF function offers a parameter k to influence its ouput, additionaly for my specific task I can also vary a window length l on which ...
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Variance in cross validation score / model selection
Between cross-validation runs of a xgboost classification model, I gather different validation scores. This is normal, the Train/validation split and model state are different each time.
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What is 'parameter convergence'?
I'm trying to teach myself data science, with my particular interest being decision trees. A few steps in, I've come across a term, 'parameter convergence' that I can't find a definition for (because, ...
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Optimal parameter estimation for a classifier with multiple parameters
The image on the left shows a standard ROC curve formed by sweeping a single threshold and recording the corresponding True Positive Rate (TPR) and False Positive Rate (FPR).
The image on the right ...
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generalized likelihood ratio test (GLRT)
I am having trouble in understanding the generalized likelihood ratio test (GLRT). Can anyone explain what it is to me, or point me toward an easy-to-understand reference? Is it a supervised or ...
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With EM algorithm, can you infer the location and variance of each "peak" in a pdf? Gaussian Mixture Models?
When I plot my data into bins, there is a frequency of data points per bin, which I can plot with a histogram. Based on this probability density function, I would like to find the maximum likelihood ...
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EM parameter estimation for conditional Gaussians
Let $$X_1\sim N(\mu_{X_1},\sigma_{X_2}^2)$$ $$X_2\sim N(\mu_{X_2},
\sigma_{X_2}^2)$$
where $\mu_{X_2}=c+aX_1$. Also, I have data $D$ (with missing values on $X_1,X_2$).
How can I update/estimate the ...
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Gibbs sampling in R
I have the following model:
$y_{it}=\alpha + x'_{it}\beta_{i} + \epsilon_{it}, \text{ }
i=1,2,...,N, \text{ } t=1,2,...,T$ (1)
$\beta_{i}= z'_{i}\gamma+\eta_{i}$ (2)
with $\epsilon_{it} \sim N(0,\...
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