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Amazon ships billions of packages to its customers annually within the United States. Shipping cost of these packages are used on the day of shipping (day 0) to estimate profitability of sales. Downstream systems utilize these days 0 profitability estimates to make financial decisions, such as pricing strategies and delisting loss-making products. However, obtaining accurate shipping cost estimates on day 0 is complex for reasons like delay in carrier invoicing or fixed cost components getting recorded at monthly cadence. Inaccurate shipping cost estimates can lead to bad decision, such as pricing items too low or high, or promoting the wrong product to the customers. Current solutions for estimating shipping costs on day 0 rely on tree-based models that require extensive manual engineering efforts. In this study, we propose a novel architecture called the Rate Card Transformer (RCT) that uses self-attention to encode all package shipping information such as package attributes, carrier information and route plan. Unlike other transformer-based tabular models, RCT has the ability to encode a variable list of one-to-many relations of a shipment, allowing it to capture more information about a shipment. For example, RCT can encode properties of all products in a package. Our results demonstrate that cost predictions made by the RCT have 28.82% less error compared to tree-based GBDT model. Moreover, the RCT outperforms the state-of-the-art transformer-based tabular model, FTTransformer, by 6.08%. We also illustrate that the RCT learns a generalized manifold of the rate card that can improve the performance of tree-based models.

Mutual information (MI) is an information-theoretic measure of dependency between two random variables. Several methods to estimate MI, from samples of two random variables with unknown underlying probability distributions have been proposed in the literature. Recent methods realize parametric probability distributions or critic as a neural network to approximate unknown density ratios. The approximated density ratios are used to estimate different variational lower bounds of MI. While these methods provide reliable estimation when the true MI is low, they produce high variance estimates in cases of high MI. We argue that the high variance characteristic is due to the uncontrolled complexity of the critic's hypothesis space. In support of this argument, we use the data-driven Rademacher complexity of the hypothesis space associated with the critic's architecture to analyse generalization error bound of variational lower bound estimates of MI. In the proposed work, we show that it is possible to negate the high variance characteristics of these estimators by constraining the critic's hypothesis space to Reproducing Hilbert Kernel Space (RKHS), which corresponds to a kernel learned using Automated Spectral Kernel Learning (ASKL). By analysing the aforementioned generalization error bounds, we augment the overall optimisation objective with effective regularisation term. We empirically demonstrate the efficacy of this regularization in enforcing proper bias variance tradeoff on four variational lower bounds, namely NWJ, MINE, JS and SMILE.

Video Prediction is an interesting and challenging task of predicting future frames from a given set context frames that belong to a video sequence. Video prediction models have found prospective applications in Maneuver Planning, Health care, Autonomous Navigation and Simulation. One of the major challenges in future frame generation is due to the high dimensional nature of visual data. In this work, we propose Mutual Information Predictive Auto-Encoder (MIPAE) framework, that reduces the task of predicting high dimensional video frames by factorising video representations into content and low dimensional pose latent variables that are easy to predict. A standard LSTM network is used to predict these low dimensional pose representations. Content and the predicted pose representations are decoded to generate future frames. Our approach leverages the temporal structure of the latent generative factors of a video and a novel mutual information loss to learn disentangled video representations. We also propose a metric based on mutual information gap (MIG) to quantitatively access the effectiveness of disentanglement on DSprites and MPI3D-real datasets. MIG scores corroborate with the visual superiority of frames predicted by MIPAE. We also compare our method quantitatively on evaluation metrics LPIPS, SSIM and PSNR.