Linear regression is a classical paradigm in statistics. A new look at it is provided via the lens of universal learning. In applying universal learning to linear regression the hypotheses class represents the label y ∈ R as a linear combination of the feature vector x T θ where x ∈ R M , within a Gaussian error. The Predictive Normalized Maximum Likelihood (pNML) solution for universal learning of individual data can be expressed analytically in this case, as well as its associated learnability measure. Interestingly, the situation where the number of parameters M may even be larger than the number of training samples N can be examined. As expected, in this case learnability cannot be attained in every situation; nevertheless, if the test vector resides mostly in a subspace spanned by the eigenvectors associated with the large eigenvalues of the empirical correlation matrix of the training data, linear regression can generalize despite the fact that it uses an "over-parametrized" model. We demonstrate the results with a simulation of fitting a polynomial to data with a possibly large polynomial degree.

Automatically understanding the contents of an image is a highly relevant problem in practice. In e-commerce and social media settings, for example, a common problem is to automatically categorize user-provided pictures. Nowadays, a standard approach is to fine-tune pre-trained image models with application-specific data. Besides images, organizations however often also collect collaborative signals in the context of their application, in particular how users interacted with the provided online content, e.g., in forms of viewing, rating, or tagging. Such signals are commonly used for item recommendation, typically by deriving latent user and item representations from the data. In this work, we show that such collaborative information can be leveraged to improve the classification process of new images. Specifically, we propose a multitask learning framework, where the auxiliary task is to reconstruct collaborative latent item representations. A series of experiments on datasets from e-commerce and social media demonstrates that considering collaborative signals helps to significantly improve the performance of the main task of image classification by up to 9.1%.

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We propose a method for specializing deep detectors and trackers to restricted settings. Our approach is designed with the following goals in mind: (a) Improving accuracy in restricted domains; (b) preventing overfitting to new domains and forgetting of generalized capabilities; (c) aggressive model compression and acceleration. To this end, we propose a novel loss that balances compression and acceleration of a deep learning model vs. loss of generalization capabilities. We apply our method to the existing tracker and detector models. We report detection results on the VIRAT and CAVIAR data sets. These results show our method to offer unprecedented compression rates along with improved detection. We apply our loss for tracker compression at test time, as it processes each video. Our tests on the OTB2015 benchmark show that applying compression during test time actually improves tracking performance.

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