Do the components of a word vector mean anything that is useful for the model to learn? I am using word embeddings as independent features to train a classifier (rf),  and I am getting validation accuracy of 75% comes close to another built using hand engineered features. I am trying to interpret feature importances given by the model—do the components of a word vector mean anything that is useful for the model to learn, or is it just noise that it has learned? The most common way I have come across people use word vector as features is by using a similarity kind of measure between vectors but here I do not have such a setup.
PS: I am using the google new word vectors of 300 dimension.
 A: Word2Vec is a technique for embedding words into a latent space of vectors, which ends up having similar-used words being close to each other. Thus you'd expect $v_{yale}$ to be close to $v_{harvard}$ and $v_{stanford}$. 
More Specifically word2vec actually preserves analogies: 
"king is to queen" as "man is to woman" is quantified as:
$$v_{king}-v_{queen} \approx v_{man}-v_{woman},$$
which allows you to say things like,
$$v_{queen}\approx v_{king}-v_{man}+v_{woman}.$$
The individual components of each $v$ do not carry an obvious meaning, but they are not noise, due to the above relations. The issue is interpretability. You could for example cluster word2vec embeddings to see which words occur close to eachother. The biggest issue here is that the embedding is calculated from random initial conditions, and is rotation and scale invariant. So if you do want to extract meaning from directions, you could do PCA on your dataset and then look at how words cluster at opposite ends of each direction.
A: If you think that entries of principal components from PCA mean something, then yes.
There is a way of viewing different word embeddings as matrix factorizations, see Levy and Goldberg's Neural Word Embedding
as Implicit Matrix Factorization.
A: Thanks Alex/Jakub. I was trying to interpret individual components of the 300 dim vector. while mathematically, it doesn't seem to capture any meaning. some of the components turned out to be important as per the model. on checking the important variables - it did make sense. For example, v252 (component of embedding) was capturing grocery related terms, similarly v75 was capturing adjectives like top, best,etc. Using word embedding features provided a 5% lift in accuracy compared to hand engineered features. 
