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Register a new userA Theoretical Framework for Target Propagation
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The success of deep learning, a brain-inspired form of AI, has sparked interest in understanding how the brain could similarly learn across multiple layers of neurons. However, the majority of biologically-plausible learning algorithms have not yet reached the performance of backpropagation (BP), nor are they built on strong theoretical foundations. Here, we analyze target propagation (TP), a popular but not yet fully understood alternative to BP, from the standpoint of mathematical optimization. Our theory shows that TP is closely related to Gauss-Newton optimization and thus substantially differs from BP. Furthermore, our analysis reveals a fundamental limitation of difference target propagation (DTP), a well-known variant of TP, in the realistic scenario of non-invertible neural networks. We provide a first solution to this problem through a novel reconstruction loss that improves feedback weight training, while simultaneously introducing architectural flexibility by allowing for direct feedback connections from the output to each hidden layer. Our theory is corroborated by experimental results that show significant improvements in performance and in the alignment of forward weight updates with loss gradients, compared to DTP.
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Humans can learn a variety of concepts and skills incrementally over the course of their lives while exhibiting many desirable properties, such as continual learning without forgetting, forward transfer and backward transfer of knowledge, and learning a new concept or task with only a few examples. Several lines of machine learning research, such as lifelong learning, few-shot learning, and transfer learning, attempt to capture these properties. However, most previous approaches can only demonstrate subsets of these properties, often by different complex mechanisms. In this work, we propose a simple yet powerful unified framework that supports almost all of these properties and approaches through one central mechanism. We also draw connections between many peculiarities of human learning (such as memory loss and rain man) and our framework. While we do not present any state-of-the-art results, we hope that this conceptual framework provides a novel perspective on existing work and proposes many new research directions.
In many applications, there is a need to predict the effect of an intervention on different individuals from data. For example, which customers are persuadable by a product promotion? which patients should be treated with a certain type of treatment? These are typical causal questions involving the effect or the change in outcomes made by an intervention. The questions cannot be answered with traditional classification methods as they only use associations to predict outcomes. For personalised marketing, these questions are often answered with uplift modelling. The objective of uplift modelling is to estimate causal effect, but its literature does not discuss when the uplift represents causal effect. Causal heterogeneity modelling can solve the problem, but its assumption of unconfoundedness is untestable in data. So practitioners need guidelines in their applications when using the methods. In this paper, we use causal classification for a set of personalised decision making problems, and differentiate it from classification. We discuss the conditions when causal classification can be resolved by uplift (and causal heterogeneity) modelling methods. We also propose a general framework for causal classification, by using off-the-shelf supervised methods for flexible implementations. Experiments have shown two instantiations of the framework work for causal classification and for uplift (causal heterogeneity) modelling, and are competitive with the other uplift (causal heterogeneity) modelling methods.
We introduce a flexible family of fairness regularizers for (linear and logistic) regression problems. These regularizers all enjoy convexity, permitting fast optimization, and they span the rang from notions of group fairness to strong individual fairness. By varying the weight on the fairness regularizer, we can compute the efficient frontier of the accuracy-fairness trade-off on any given dataset, and we measure the severity of this trade-off via a numerical quantity we call the Price of Fairness (PoF). The centerpiece of our results is an extensive comparative study of the PoF across six different datasets in which fairness is a primary consideration.
Generative adversarial network (GAN) is a minimax game between a generator mimicking the true model and a discriminator distinguishing the samples produced by the generator from the real training samples. Given an unconstrained discriminator able to approximate any function, this game reduces to finding the generative model minimizing a divergence measure, e.g. the Jensen-Shannon (JS) divergence, to the data distribution. However, in practice the discriminator is constrained to be in a smaller class $mathcal{F}$ such as neural nets. Then, a natural question is how the divergence minimization interpretation changes as we constrain $mathcal{F}$. In this work, we address this question by developing a convex duality framework for analyzing GANs. For a convex set $mathcal{F}$, this duality framework interprets the original GAN formulation as finding the generative model with minimum JS-divergence to the distributions penalized to match the moments of the data distribution, with the moments specified by the discriminators in $mathcal{F}$. We show that this interpretation more generally holds for f-GAN and Wasserstein GAN. As a byproduct, we apply the duality framework to a hybrid of f-divergence and Wasserstein distance. Unlike the f-divergence, we prove that the proposed hybrid divergence changes continuously with the generative model, which suggests regularizing the discriminators Lipschitz constant in f-GAN and vanilla GAN. We numerically evaluate the power of the suggested regularization schemes for improving GANs training performance.
We study bandits and reinforcement learning (RL) subject to a conservative constraint where the agent is asked to perform at least as well as a given baseline policy. This setting is particular relevant in real-world domains including digital marketing, healthcare, production, finance, etc. For multi-armed bandits, linear bandits and tabular RL, specialized algorithms and theoretical analyses were proposed in previous work. In this paper, we present a unified framework for conservative bandits and RL, in which our core technique is to calculate the necessary and sufficient budget obtained from running the baseline policy. For lower bounds, our framework gives a black-box reduction that turns a certain lower bound in the nonconservative setting into a new lower bound in the conservative setting. We strengthen the existing lower bound for conservative multi-armed bandits and obtain new lower bounds for conservative linear bandits, tabular RL and low-rank MDP. For upper bounds, our framework turns a certain nonconservative upper-confidence-bound (UCB) algorithm into a conservative algorithm with a simple analysis. For multi-armed bandits, linear bandits and tabular RL, our new upper bounds tighten or match existing ones with significantly simpler analyses. We also obtain a new upper bound for conservative low-rank MDP.
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