In the realm of deep learning, the Fisher information matrix (FIM) gives novel insights and useful tools to characterize the loss landscape, perform second-order optimization, and build geometric learning theories. The exact FIM is either unavailable in closed form or too expensive to compute. In practice, it is almost always estimated based on empirical samples. We investigate two such estimators based on two equivalent representations of the FIM -- both unbiased and consistent. Their estimation quality is naturally gauged by their variance given in closed form. We analyze how the parametric structure of a deep neural network can affect the variance. The meaning of this variance measure and its upper bounds are then discussed in the context of deep learning.

Experimental results on both synthetic and real data demonstrate theefficacyoftheproposed frameworkfordomain adaptation.

Built upon this foundation, recent studies further highlight the importance of grouping semantically similar instances. One effective method to achieve this is by promoting the semantic structure preserved by neighborhood consistency.

Moreoverkappr K, is squared FrkapproximationA, i.e., min Examining 3, left), it sharperpeakk, whereas resultsinthe1.

There are two well-known techniques, called Value at Risk (VaR, or Quantile) and Conditional Value at Risk (CVaR), to manage undesirable events in the domain of finance[18].

InBiauetal.(2008),theyemploy the randomized sketches method to project the data in Hilbert space so as to approximate kernel k-means. However, the data in Hilbert space are implicit and infinite-dimensional, and its sketch matrixisdenseandunstructured.

InBiauetal.(2008),theyemploy the randomized sketches method to project the data in Hilbert space so as to approximate kernel k-means. However, the data in Hilbert space are implicit and infinite-dimensional, and its sketch matrixisdenseandunstructured.

Graph contrastivelearning attracts/disperses node representations forsimilar/dissimilar node pairs under some notion of similarity.