Daily TMLR digest for Mar 09, 2023
TMLR
Accepted papers
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Title: Costs and Benefits of Fair Regression
Authors: Han Zhao
Abstract: Real-world applications of machine learning tools in high-stakes domains are often regulated to be fair, in the sense that the predicted target should satisfy some quantitative notion of parity with respect to a protected attribute. However, the exact tradeoff between fairness and accuracy with a real-valued target is not entirely clear. In this paper, we characterize the inherent tradeoff between statistical parity and accuracy in the regression setting by providing a lower bound on the error of any attribute-blind fair regressor. Our lower bound is sharp, algorithm-independent, and admits a simple interpretation: when the moments of the target differ between groups, any fair algorithm has to make an error on at least one of the groups. We further extend this result to give a lower bound on the joint error of any (approximately) fair algorithm, using the Wasserstein distance to measure the quality of the approximation. With our novel lower bound, we also show that the price paid by a fair regressor that does not take the protected attribute as input is less than that of a fair regressor with explicit access to the protected attribute. On the upside, we establish the first connection between individual fairness, accuracy parity, and the Wasserstein distance by showing that if a regressor is individually fair, it also approximately verifies the accuracy parity, where the gap is again given by the Wasserstein distance between the two groups. Inspired by our theoretical results, we develop a practical algorithm for fair regression through the lens of representation learning, and conduct experiments on a real-world dataset to corroborate our findings.
URL: https://openreview.net/forum?id=v6anjyEDVW
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Title: Transfer Entropy Bottleneck: Learning Sequence to Sequence Information Transfer
Authors: Damjan Kalajdzievski, Ximeng Mao, Pascal Fortier-Poisson, Guillaume Lajoie, Blake Aaron Richards
Abstract: When presented with a data stream of two statistically dependent variables, predicting the future of one of the variables (the target stream) can benefit from information about both its history and the history of the other variable (the source stream). For example, fluctuations in temperature at a weather station can be predicted using both temperatures and barometric readings. However, a challenge when modelling such data is that it is easy for a neural network to rely on the greatest joint correlations within the target stream, which may ignore a crucial but small information transfer from the source to the target stream. As well, there are often situations where the target stream may have previously been modelled independently and it would be useful to use that model to inform a new joint model. Here, we develop an information bottleneck approach for conditional learning on two dependent streams of data. Our method, which we call Transfer Entropy Bottleneck (TEB), allows one to learn a model that bottlenecks the directed information transferred from the source variable to the target variable, while quantifying this information transfer within the model. As such, TEB provides a useful new information bottleneck approach for modelling two statistically dependent streams of data in order to make predictions about one of them.
URL: https://openreview.net/forum?id=kJcwlP7BRs
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Title: Transductive Decoupled Variational Inference for Few-Shot Classification
Authors: Anuj Rajeeva Singh, Hadi Jamali-Rad
Abstract: The versatility to learn from a handful of samples is the hallmark of human intelligence. Few-shot learning is an endeavour to transcend this capability down to machines. Inspired by the promise and power of probabilistic deep learning, we propose a novel variational inference network for few-shot classification (coined as TRIDENT) to decouple the representation of an image into semantic and label latent variables, and simultaneously infer them in an intertwined fashion. To induce task-awareness, as part of the inference mechanics of TRIDENT, we exploit information across both query and support images of a few-shot task using a novel built-in attention-based transductive feature extraction module (we call AttFEX). Our extensive experimental results corroborate the efficacy of TRIDENT and demonstrate that, using the simplest of backbones, it sets a new state-of-the-art in the most commonly adopted datasets miniImageNet and tieredImageNet (offering up to 4% and 5% improvements, respectively), as well as for the recent challenging cross-domain miniImagenet --> CUB scenario offering a significant margin (up to 20% improvement) beyond the best existing baselines.
URL: https://openreview.net/forum?id=bomdTc9HyL
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New submissions
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Title: TESH-GCN: Text Enriched Sparse Hyperbolic Graph Convolutional Networks
Abstract: Heterogeneous networks, which connect informative nodes containing semantic information with different edge types, are routinely used to store and process information in various real-world applications. Graph Neural Networks (GNNs) and their hyperbolic variants provide a promising approach to encode such networks in a low-dimensional latent space through neighborhood aggregation and hierarchical feature extraction, respectively. However, these approaches typically ignore metapath structures and the available semantic information. Furthermore, these approaches are sensitive to the noise present in the training data. To tackle these limitations, in this paper, we propose Text Enriched Sparse Hyperbolic Graph Convolution Network (TESH-GCN). In TESH-GCN, we use semantic node information to identify relevant nodes and extract their local neighborhood and graph-level metapath features. This is done by applying a reformulated hyperbolic graph convolution layer to the sparse adjacency tensor using the semantic node information as a connection signal. These extracted features in conjunction with semantic features from the language model (for robustness) are used for the final downstream tasks. Experiments on various heterogeneous graph datasets show that our model outperforms the state-of-the-art approaches by a large margin on the task of link prediction. We also report a reduction in both the training time and model parameters compared to the existing hyperbolic approaches through a reformulated hyperbolic graph convolution. Furthermore, we illustrate the robustness of our model by experimenting with different levels of simulated noise in both the graph structure and text, and also, present a mechanism to explain TESH-GCN’s prediction by analyzing the extracted metapaths.
URL: https://openreview.net/forum?id=Z4UPS80y3O
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Title: The Geometry of Mixability
Abstract: Mixable loss functions are of fundamental importance in the context of prediction with expert advice in the online setting since they characterize fast learning rates. By re-interpreting properness from the point of view of differential geometry, we provide a simple geometric characterization of mixability for the binary and multi-class cases: a proper loss function $\ell$ is $\eta$-mixable if and only if the superpredition set $\textrm{spr}(\eta \ell)$ of the scaled loss function $\eta \ell$ slides freely inside the superprediction set $\textrm{spr}(\ell_{\log})$ of the log loss $\ell_{\log}$, under fairly general assumptions on the differentiability of $\ell$. Our approach provides a way to treat some concepts concerning loss functions (like properness) in a ''coordinate-free'' manner and reconciles previous results obtained for mixable loss functions for the binary and the multi-class cases.
URL: https://openreview.net/forum?id=VrvGHDSzZ7
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