Answers.Body: <p>Indeed the choice of representation can introduce additional inductive biases beyond the bias introduced by the learning algorithm itself such as your linear regression model example. The key idea here is that the features you represent shape the hypothesis space that the learner explores, and this can affect which hypotheses are more likely to be preferred or even possible within that space.</p>
  <p>For your example, the second representation's relationship between distance from the city center or number of swimming pools and house price is intuitively complex and nonlinear, the linear model might struggle to fit the data, and you're very likely to see poor performance. Thus by choosing a particular representation of the raw data, you are <em>implicitly introducing</em> constraints on the types of hypotheses that are possible within the entire hypotheses space. And in general ML algos like decision trees also implicitly introduce inductive biases such as favoring more simple shallower trees.</p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2024-09-15T17:58:39.443Z
Answers.Text: Thanks for this answer! I think the crux lies in "Thus by choosing **a particular representation of the raw data**" (emphasis mine). So we need to assume a raw input space, right?
Answers.UserDisplayName: Antonios Sarikas
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2024-09-16T17:58:51.583Z
Answers.Text: @adosar Yes otherwise you're completely agnostic. And bear in mind some people would call raw data as representation too. Hope this clarifies.
Answers.UserDisplayName: cinch
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2024-09-14T21:47:16.350Z
Answers.LastActivityDate: 2024-09-14T21:47:16.350Z
Answers.UserDisplayName: cinch
Answers.Body: <p>Yes, representations in machine learning introduce inductive biases. Inductive bias refers to the assumptions a model makes to generalize from limited data. Representations are how data is structured or encoded for input into a model, and these representations inherently carry assumptions about the nature of the data and the relationships within it.</p>
  <p>For example:</p>
  <ul>
  <li><strong>Handcrafted Features</strong>: When you manually design features, you're embedding assumptions about what aspects of the data are important (e.g., edge detection in image processing or n-grams in text analysis).</li>
  <li><strong>Learned Representations</strong>: In models like neural networks, the architecture and the way features are extracted (e.g., convolutional layers in CNNs) impose inductive biases. For instance, CNNs assume that nearby pixels in an image have related information.</li>
  </ul>
  <p>Thus, the choice of representation influences the types of patterns the model can learn, impacting the inductive biases introduced into the learning process. A best <a href="https://leaveit2ai.com/" rel="nofollow noreferrer">ai video generator</a> is explaining it at the destination</p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2024-09-15T18:02:18.133Z
Answers.Text: ali Welcome to the community and thanks for this answer! "Representations are how data is structured or encoded". You are referring to representations of **raw data**, right?
Answers.UserDisplayName: Antonios Sarikas
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2024-09-15T06:14:05.697Z
Answers.LastActivityDate: 2024-09-15T06:14:05.697Z
Answers.UserDisplayName:  naqcho ali
Body: <p>I am trying to get a better understanding of inductive biases used in machine learning.</p>
  <p>I understand inductive biases as the assumptions encoded into the learning algorithm which make it prefer one hypothesis over another.</p>
  <p>Architectural choices are prime examples of inductive biases. The simplest example, linear regression, assumes that there is a linear relationship between input and output.</p>
  <p>My question is whether the choice of representation forces the algorithm to prefer one hypothesis over another.</p>
  <p><strong>Simple example</strong></p>
  <p>Suppose that our problem is to predict house prices. We can select between 2 different representations:</p>
  <ol>
  <li>House is represented as: <span class="math-container">$(x_1, x_2) \gets $</span> (area of house, # bedrooms)</li>
  <li>House is represented as: <span class="math-container">$(x_1', x_2') \gets $</span> (distance from city center, # swimming pools)</li>
  </ol>
  <p>Does the choice of representation introduce any additional inductive bias besides the one introduced by linear regression? I mean in both cases, we are left with mapping from <span class="math-container">$\mathbb{R}^2 \to \mathbb{R}$</span> with a linear function.</p>
  <p><strong>My view (possibly wrong)</strong></p>
  <p>The only way I can think of representations introducing an inductive bias is if we view the problem as following. There is an input space <span class="math-container">$X$</span> (the raw input) and we are interested in finding a map <span class="math-container">$X \to Y$</span>. If we use a learner with <span class="math-container">$(x_1, x_2)$</span>, then this amounts to finding a function:</p>
  <p><span class="math-container">$X \to g(X) \to h(g(X)) \to Y$</span></p>
  <p>where <span class="math-container">$(x_1, x_2) = g(X)$</span>. Now we have an inductive bias, since the function the learner must pick is the total composition <span class="math-container">$h(g(X))$</span> and the constraint arises since it must include <span class="math-container">$g(X)$</span>.</p>
  
Tags: <machine-learning><generalization><inductive-bias>
Title: Do representations introduce an inductive bias?
UserDisplayName: Antonios Sarikas
ThreadText: # Do representations introduce an inductive bias?
  
  (Asked by: username_0 on 2024-09-12)
  
  I am trying to get a better understanding of inductive biases used in machine learning.
  
  I understand inductive biases as the assumptions encoded into the learning algorithm which make it prefer one hypothesis over another.
  
  Architectural choices are prime examples of inductive biases. The simplest example, linear regression, assumes that there is a linear relationship between input and output.
  
  My question is whether the choice of representation forces the algorithm to prefer one hypothesis over another.
  
  **Simple example**
  
  Suppose that our problem is to predict house prices. We can select between 2 different representations:
  
  1. House is represented as: $(x\_1, x\_2) \gets $ (area of house, # bedrooms)
  2. House is represented as: $(x\_1', x\_2') \gets $ (distance from city center, # swimming pools)
  
  Does the choice of representation introduce any additional inductive bias besides the one introduced by linear regression? I mean in both cases, we are left with mapping from $\mathbb{R}^2 \to \mathbb{R}$ with a linear function.
  
  **My view (possibly wrong)**
  
  The only way I can think of representations introducing an inductive bias is if we view the problem as following. There is an input space $X$ (the raw input) and we are interested in finding a map $X \to Y$. If we use a learner with $(x\_1, x\_2)$, then this amounts to finding a function:
  
  $X \to g(X) \to h(g(X)) \to Y$
  
  where $(x\_1, x\_2) = g(X)$. Now we have an inductive bias, since the function the learner must pick is the total composition $h(g(X))$ and the constraint arises since it must include $g(X)$.
  
  **Tags:** machine-learning, generalization, inductive-bias
  
  
  ---
  
  ## 2 answers
  
  ### Answer by username_1 on 2024-09-14. Score: 1 | Accepted answer
  
  Indeed the choice of representation can introduce additional inductive biases beyond the bias introduced by the learning algorithm itself such as your linear regression model example. The key idea here is that the features you represent shape the hypothesis space that the learner explores, and this can affect which hypotheses are more likely to be preferred or even possible within that space.
  
  For your example, the second representation's relationship between distance from the city center or number of swimming pools and house price is intuitively complex and nonlinear, the linear model might struggle to fit the data, and you're very likely to see poor performance. Thus by choosing a particular representation of the raw data, you are *implicitly introducing* constraints on the types of hypotheses that are possible within the entire hypotheses space. And in general ML algos like decision trees also implicitly introduce inductive biases such as favoring more simple shallower trees.
  
  > **Comments:**
  > **username_0**: Thanks for this answer! I think the crux lies in "Thus by choosing **a particular representation of the raw data**" (emphasis mine). So we need to assume a raw input space, right?  
  > **username_1**: @adosar Yes otherwise you're completely agnostic. And bear in mind some people would call raw data as representation too. Hope this clarifies.  
  
  ---
  
  ### Answer by username_2 on 2024-09-15. Score: 2
  
  Yes, representations in machine learning introduce inductive biases. Inductive bias refers to the assumptions a model makes to generalize from limited data. Representations are how data is structured or encoded for input into a model, and these representations inherently carry assumptions about the nature of the data and the relationships within it.
  
  For example:
  
  * **Handcrafted Features**: When you manually design features, you're embedding assumptions about what aspects of the data are important (e.g., edge detection in image processing or n-grams in text analysis).
  * **Learned Representations**: In models like neural networks, the architecture and the way features are extracted (e.g., convolutional layers in CNNs) impose inductive biases. For instance, CNNs assume that nearby pixels in an image have related information.
  
  Thus, the choice of representation influences the types of patterns the model can learn, impacting the inductive biases introduced into the learning process. A best [ai video generator](https://leaveit2ai.com/) is explaining it at the destination
  
  > **Comments:**
  > **username_0**: ali Welcome to the community and thanks for this answer! "Representations are how data is structured or encoded". You are referring to representations of **raw data**, right?  
  
  ---
  
  