Caveats for information bottleneck in deterministic scenarios

Information bottleneck (IB) is a method for extracting information from one random variable $X$ that is relevant for predicting another random variable $Y$. To do so, IB identifies an intermediate "bottleneck" variable $T$ that has low mutual information $I(X;T)$ and high mutual information $I(Y;T)$. The "IB curve" characterizes the set of bottleneck variables that achieve maximal $I(Y;T)$ for a given $I(X;T)$, and is typically explored by maximizing the "IB Lagrangian", $I(Y;T) - \beta I(X;T)$. In some cases, $Y$ is a deterministic function of $X$, including many classification problems in supervised learning where the output class $Y$ is a deterministic function of the input $X$. We demonstrate three caveats when using IB in any situation where $Y$ is a deterministic function of $X$: (1) the IB curve cannot be recovered by maximizing the IB Lagrangian for different values of $\beta$; (2) there are "uninteresting" trivial solutions at all points of the IB curve; and (3) for multi-layer classifiers that achieve low prediction error, different layers cannot exhibit a strict trade-off between compression and prediction, contrary to a recent proposal. We also show that when $Y$ is a small perturbation away from being a deterministic function of $X$, these three caveats arise in an approximate way. To address problem (1), we propose a functional that, unlike the IB Lagrangian, can recover the IB curve in all cases. We demonstrate the three caveats on the MNIST dataset

CuisineNet: Food Attributes Classification using Multi-scale Convolution Network

Diversity of food and its attributes represents the culinary habits of peoples from different countries. Thus, this paper addresses the problem of identifying food culture of people around the world and its flavor by classifying two main food attributes, cuisine and flavor. A deep learning model based on multi-scale convotuional networks is proposed for extracting more accurate features from input images. The aggregation of multi-scale convolution layers with different kernel size is also used for weighting the features results from different scales. In addition, a joint loss function based on Negative Log Likelihood (NLL) is used to fit the model probability to multi labeled classes for multi-modal classification task. Furthermore, this work provides a new dataset for food attributes, so-called Yummly48K, extracted from the popular food website, Yummly. Our model is assessed on the constructed Yummly48K dataset. The experimental results show that our proposed method yields 65% and 62% average F1 score on validation and test set which outperforming the state-of-the-art models.Comment: 8 pages, Submitted in CCIA 201