Let ˆf: X 7 Y where ˆf = ˆh g with g: X 7 Z and ˆh: Z 7 Y . Corollary 2. Consider a domainD = (P,f) with data distributionP and ground-truth labeling functionf. A hypothesis is ˆf: X 7 Y, where ˆf = ˆh g withg: X 7 Z and ˆh: Z 7 Y . Here, thiskind ofbound isdeveloped using data distributionPoninput space andlabeling functionf from input tolabel space, which arenot convenient in understanding representation learning, sincePT,PS are data nature and therefore fixed. Theorem 3. (Theorem 1 in the main paper) Consider a mixture of source domainsDπ = Next, we relate the loss on targetDTg to hybrid domain Dhyg, which differs only at the feature marginals. In other words, the equality happens when all distributions are the sameQ1=...=QC.

Domain adaptation (DA) is a specific case of MSDA when we need to transfer from a single source domain to an another target domain available during training.

When data values are`2-normalized, our algorithm iteratively computes the top eigenvector of a sequence of matrices, and does not lose any multiplicativeapproximation factor.

Socialbiasinmachine learning hasdrawnsignificant attention, withworkranging from demonstrations of bias in a multitude of applications, curating definitions of fairness for different contexts, to developing algorithms to mitigate bias. In natural language processing, gender bias has been shown to exist in context-free word embeddings. Recently, contextual word representations have outperformed word embeddings in several downstream NLP tasks.

AwidevarietyofNLPapplications, suchasmachinetranslation, summarization, and dialog, involve text generation. One major challenge for these applications is how to evaluate whether such generated texts are actually fluent, accurate, or effective. In this work, we conceptualize theevaluation of generated text as a text generation problem, modeled using pre-trained sequence-to-sequence models. The general idea is that models trained to convert the generated text to/from a reference output or the source text will achieve higher scores when the generated text is better.