The aim is to design truthful mechanisms, ensuring agents cannot gain by misreporting.

The prediction concatenation (PreConc) operation is crucial for the multi-layer feature transformation in deep forest, though little has been known about its theoretical property.

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.

Learning to accurately represent environmental uncertainty is crucial for adaptive and optimal behaviors in various cognitive tasks. However, it remains unclear how the human brain, constrained by finite cognitive resources, internalise the highly structured environmental uncertainty. In this study, we explore how these learned distributions deviate from the ground truth, resulting in observable inconsistency in a novel structured density estimation task. During each trial, human participants were asked to learn and report the latent probability distribution functions underlying sequentially presented independent observations. As the number of observations increased, the reported predictive density became closer to the ground truth. Nevertheless, we observed an intriguing inconsistency in human structure estimation, specifically a large error in the number of reported clusters.

Privacy issue is a main concern in developing face recognition techniques.