Question: What is the difference between the Bayesian Inference and other machine learning techniques?
Evidence: Bayesian Inference differs from other machine learning techniques by introducing a distribution INLINEFORM0 over the parameters of the model. A major concern in Bayesian Inference is usually to define a prior that makes as little assumption as possible. Such a prior is usually known as uninformative prior. Having a completely uninformative prior has the practical advantage that the prior distribution will have a minimal impact on the outcome of the inference leading to a model which bases its prediction purely and solely on the data. In the present work, we aim at the opposite behavior, we wish our AUD model to learn phone-like units from the unlabeled speech data of a target language given the knowledge that was previously accumulated from another resourceful language. More formally, the original AUD model training consists in estimate the a posteriori distribution of the parameters given the unlabeled speech data of a target language INLINEFORM1 : DISPLAYFORM0 
The parameters are divided into two subgroups INLINEFORM0 where INLINEFORM1 are the global parameters of the model, and INLINEFORM2 are the latent variables which, in our case, correspond to the sequences of acoustic units. The global parameters are separated into two independent subsets : INLINEFORM3 , corresponding to the acoustic parameters ( INLINEFORM4 ) and the "phonotactic" language model parameters ( INLINEFORM5 ). Replacing INLINEFORM6 and following the conditional independence of the variable induced by the model (see BIBREF1 for details) leads to: DISPLAYFORM0 
If we further assume that we have at our disposal speech data in a different language than the target one, denoted INLINEFORM0 , along with its phonetic transcription INLINEFORM1 , it is then straightforward to show that: DISPLAYFORM0 
 which is the same as Eq. EQREF8 but for the distribution of the acoustic parameters which is based on the data of the resourceful language. In contrast of the term uninformative prior we denote INLINEFORM0 as an informative prior. As illustrated by Eq. EQREF9 , a characteristic of Bayesian inference is that it naturally leads to a sequential inference. Therefore, model training can be summarized as:
Practically, the computation of the informative prior as well as the final posterior distribution is intractable and we seek for an approximation by means of the well known Variational Bayes Inference BIBREF12 . The approximate informative prior INLINEFORM0 is estimated by optimizing the variational lower bound of the evidence of the prior data INLINEFORM1 : DISPLAYFORM0 
where INLINEFORM0 is the Kullback-Leibler divergence. Then, the posterior distribution of the parameters given the target data INLINEFORM1 can be estimated by optimizing the evidence of the target data INLINEFORM2 : DISPLAYFORM0 
Note that when the model is trained with an uninformative prior the loss function is the as in Eq. EQREF13 but with INLINEFORM0 instead of the INLINEFORM1 . For the case of the uninformative prior, the Variational Bayes Inference was initialized as described in BIBREF1 . In the informative prior case, we initialized the algorithm by setting INLINEFORM2 .
Bayesian Inference differs from other machine learning techniques by introducing a distribution p(ξ) over the parameters of the model.
Answer: Bayesian Inference differs from other machine learning techniques by introducing a distribution p(ξ) over the parameters of the model.