Answers.Body: <p>Both statistical and deep learning models <strong>usually</strong> have parameters size that depends on the number of features of the input data when doing supervised learning. Note that this is a very high-level answer and there might be specific models that have params size depending on the number of data points as well.</p>
  <p>Let me give you a basic example to clarify the above:</p>
  <p>For a simple multivariate linear regression, we use a linear model denoted as <span class="math-container">$f(x_i)$</span> and parametrized by <span class="math-container">$\theta = (\theta_0, \ldots, \theta_d)$</span> where <span class="math-container">$d$</span> is the number of features of each data points <span class="math-container">$x_i$</span>. The model is also perturbed by some Gaussian noise <span class="math-container">$\epsilon_i \sim \mathcal{N}(0, \sigma)$</span>, also called error. Overall it is defined as:</p>
  <p><span class="math-container">\begin{equation}
  \hat{y_i} = f(x_i; \theta) + \epsilon_i := \langle \theta,  x_{i} \rangle + \epsilon_i
  \end{equation}</span></p>
  <p>The objective of the learning phase is now to fit the parameter <span class="math-container">$\theta$</span> in order to minimise the discrepancy between the predictions <span class="math-container">$\hat{y}_i$</span> and sone ground truth labels. The only parameters you can tune in this model are precisely the entries of the vector <span class="math-container">$\theta$</span>, which is of size <span class="math-container">$d$</span>.</p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2022-08-13T13:26:37.033Z
Answers.LastActivityDate: 2022-08-13T13:27:55.157Z
Answers.LastEditDate: 2022-08-13T13:27:55.157Z
Answers.UserDisplayName: Dime
Body: <p>Some online answers about parameters in machine learning mention that it is dependent on the size of dataset we have (if it is a large dataset or not). Is this size related to the number of samples we have or to the number of features for each sample, or both?</p>
  
Tags: <machine-learning><deep-learning><datasets>
Title: Meaning of Large Dataset for machine learning
UserDisplayName: Batoul Diab
ThreadText: # Meaning of Large Dataset for machine learning
  
  (Asked by: username_0 on 2022-08-11)
  
  Some online answers about parameters in machine learning mention that it is dependent on the size of dataset we have (if it is a large dataset or not). Is this size related to the number of samples we have or to the number of features for each sample, or both?
  
  **Tags:** machine-learning, deep-learning, datasets
  
  
  ---
  
  ## 1 answers
  
  ### Answer by username_1 on 2022-08-13. Score: 0 | Accepted answer
  
  Both statistical and deep learning models **usually** have parameters size that depends on the number of features of the input data when doing supervised learning. Note that this is a very high-level answer and there might be specific models that have params size depending on the number of data points as well.
  
  Let me give you a basic example to clarify the above:
  
  For a simple multivariate linear regression, we use a linear model denoted as $f(x\_i)$ and parametrized by $\theta = (\theta\_0, \ldots, \theta\_d)$ where $d$ is the number of features of each data points $x\_i$. The model is also perturbed by some Gaussian noise $\epsilon\_i \sim \mathcal{N}(0, \sigma)$, also called error. Overall it is defined as:
  
  \begin{equation}
  \hat{y\_i} = f(x\_i; \theta) + \epsilon\_i := \langle \theta, x\_{i} \rangle + \epsilon\_i
  \end{equation}
  
  The objective of the learning phase is now to fit the parameter $\theta$ in order to minimise the discrepancy between the predictions $\hat{y}\_i$ and sone ground truth labels. The only parameters you can tune in this model are precisely the entries of the vector $\theta$, which is of size $d$.
  
  
  ---
  
  