Let’s break down how you can use logistic regression, naive Bayes, and word vectors for three common Natural Language Processing (NLP) tasks: sentiment analysis, completing analogies, and translating words.

1. Sentiment Analysis:

   • Logistic Regression: For sentiment analysis, you can use logistic regression as a binary classifier to predict whether a given text has positive or negative sentiment. You would first preprocess the text (tokenization, normalization, etc.), then represent each word as a feature (using Bag-of-Words, TF-IDF, or word embeddings). Finally, train the logistic regression model on labeled data (sentiment-labeled texts) to learn the relationship between the features and the sentiment labels.
   • Naive Bayes: Similarly, you can use naive Bayes for sentiment analysis. Naive Bayes assumes independence between features, so it’s often used with Bag-of-Words or TF-IDF representations. You calculate the probabilities of each class (positive or negative sentiment) given the features, and then use Bayes’ theorem to make predictions.
   • Word Vectors: Word embeddings like Word2Vec or GloVe can capture semantic relationships between words. You can average the word vectors of all words in a sentence to get a fixed-length vector representation of the text. Then, you can feed these representations into a classifier (e.g., logistic regression or neural network) to perform sentiment analysis.

2. Completing Analogies:

   • Word Vectors: Word embeddings are often used for completing analogies. For example, if you have the analogy “man is to woman as king is to ___”, you can find the vector representation of “woman” – “man” + “king”. This results in a vector that ideally represents the word for queen. You then find the word in your vocabulary closest to this resulting vector using cosine similarity or other distance metrics.

3. Translating Words:

   • Word Vectors: You can use word embeddings for translating words by finding the nearest neighbor in the embedding space. For example, if you want to translate a word from one language to another, you can find the closest word in the embedding space of the target language. This method works well for simple translations but may not capture more complex nuances of translation.
   • Machine Translation Models: For more advanced translation tasks, you would typically use machine translation models such as sequence-to-sequence models (e.g., using an encoder-decoder architecture with attention mechanisms). These models are trained on parallel corpora (pairs of sentences in different languages) and can learn to generate translations from one language to another.

Remember that the choice of method depends on the specific task requirements, available data, and computational resources. Additionally, more advanced techniques such as deep learning models (e.g., recurrent neural networks, transformers) are commonly used for NLP tasks and may outperform traditional methods in certain scenarios.