True. In a Gaussian Mixture Model (GMM), the mixture weights associated with each Gaussian component represent the proportion of each component in the overall model.

1. **Understanding GMM Weights**: Each Gaussian component is assigned a weight, which indicates its importance or contribution to the model. These weights are typically denoted as $ w_k $, where $ k $ indicates the $ k $-th component of the mixture.

2. **Normalization Condition**: To ensure that these weights make sense in the context of probabilities, they must satisfy the normalization condition. This means that the sum of all weights must equal 1, expressed mathematically as:
$$
\sum_{k=1}^{K} w_k = 1
$$
where $ K $ is the total number of components in the GMM.

3. **Interpretation**: This condition ensures that when you take a sample from the GMM, the probability of drawing a sample is distributed according to the relative weights of the Gaussian components—effectively behaving like a probability distribution.

In summary, the statement is true: the weights of all Gaussian components in a GMM must always sum to one, ensuring that they collectively represent a valid probability distribution.

Question

True. In a Gaussian Mixture Model (GMM), the mixture weights associated with each Gaussian component represent the proportion of each component in the overall model.

1. **Understanding GMM Weights**: Each Gaussian component is assigned a weight, which indicates its importance or contribution to the model. These weights are typically denoted as $ w_k $, where $ k $ indicates the $ k $-th component of the mixture.

2. **Normalization Condition**: To ensure that these weights make sense in the context of probabilities, they must satisfy the normalization condition. This means that the sum of all weights must equal 1, expressed mathematically as:
   $$
   \sum_{k=1}^{K} w_k = 1
   $$
   where $ K $ is the total number of components in the GMM.

3. **Interpretation**: This condition ensures that when you take a sample from the GMM, the probability of drawing a sample is distributed according to the relative weights of the Gaussian components—effectively behaving like a probability distribution.

In summary, the statement is true: the weights of all Gaussian components in a GMM must always sum to one, ensuring that they collectively represent a valid probability distribution.

Knowee AI · Accepted Answer

True. In a Gaussian Mixture Model (GMM), the mixture weights associated with each Gaussian component represent the proportion of each component in the overall model.

1. **Understanding GMM Weights**: Each Gaussian component is assigned a weight, which indicates its importance or contribution to the model. These weights are typically denoted as $ w_k $, where $ k $ indicates the $ k $-th component of the mixture.

2. **Normalization Condition**: To ensure that these weights make sense in the context of probabilities, they must satisfy the normalization condition. This means that the sum of all weights must equal 1, expressed mathematically as:
   $$
   \sum_{k=1}^{K} w_k = 1
   $$
   where $ K $ is the total number of components in the GMM.

3. **Interpretation**: This condition ensures that when you take a sample from the GMM, the probability of drawing a sample is distributed according to the relative weights of the Gaussian components—effectively behaving like a probability distribution.

In summary, the statement is true: the weights of all Gaussian components in a GMM must always sum to one, ensuring that they collectively represent a valid probability distribution.

True or false: The sum of the weights of all Gaussian components in a GMM is always equal to one.TrueFalse

Question

True or false: The sum of the weights of all Gaussian components in a GMM is always equal to one.

Solution

Similar Questions

Upgrade your grade with Knowee