In many learning problems, ranging from clustering to ranking through metric learning, empirical estimates of the risk functional consist of an average over tu-ples ( e.g., pairs or triplets) of observations, rather than over individual observations. In this paper, we focus on how to best implement a stochastic approximation approach to solve such risk minimization problems. We argue that in the large-scale setting, gradient estimates should be obtained by sampling tuples of data points with replacement ( incomplete U -statistics) instead of sampling data points without replacement ( complete U -statistics based on subsamples). We develop a theoretical framework accounting for the substantial impact of this strategy on the generalization ability of the prediction model returned by the Stochastic Gradient Descent (SGD) algorithm. It reveals that the method we promote achieves a much better trade-off between statistical accuracy and computational cost. Beyond the rate bound analysis, experiments on AUC maximization and metric learning provide strong empirical evidence of the superiority of the proposed approach.

Normalizing flows have shown great promise for modelling flexible probability distributions in a computationally tractable way.

While the primary concern in this domain is usually to find realizable representations (i.e., those that allow predicting the reward function at any context-action

When using the robust performance metric described in Section 4.2, we have We solve the above linear program to obtain the results presented in Section 5.1. Work done while at UT Austin. We use Scipy's linear programming software (v 1.4.1) MDP is solved to obtain the sample's likelihood and determine the transition probabilities within the Markov chain. We used a learning rate of 0.01.

One of the central questions in statistical learning theory is to determine the conditions under which agents can learn from experience. This includes the necessary and sufficient conditions for generalization from a given finite training set to new observations. In this paper, we prove that algorithmic stability in the inference process is equivalent to uniform generalization across all parametric loss functions. We provide various interpretations of this result. For instance, a relationship is proved between stability and data processing, which reveals that algorithmic stability can be improved by post-processing the inferred hypothesis or by augmenting training examples with artificial noise prior to learning. In addition, we establish a relationship between algorithmic stability and the size of the observation space, which provides a formal justification for dimensionality reduction methods. Finally, we connect algorithmic stability to the size of the hypothesis space, which recovers the classical P AC result that the size (complexity) of the hypothesis space should be controlled in order to improve algorithmic stability and improve generalization.

We hereby provide a summarizing figure of the training and inference stages used in TIM. Figure 2: Outline of TIM framework (best viewed in color).

We introduce Transductive Infomation Maximization (TIM) for few-shot learning.