We consider the parametric learning problem, where the objective of the learner is determined by a parametric loss function. Employing empirical risk minimization with possibly regularization, the inferred parameter vector will be biased toward the training samples. Such bias is measured by the cross validation procedure in practice where the data set is partitioned into a training set used for training and a validation set, which is not used in training and is left to measure the outof-sample performance. A classical cross validation strategy is the leave-one-out cross validation (LOOCV) where one sample is left out for validation and training is done on the rest of the samples that are presented to the learner, and this process is repeated on all of the samples. LOOCV is rarely used in practice due to the high computational complexity. In this paper, we first develop a computationally efficient approximate LOOCV (ALOOCV) and provide theoretical guarantees for its performance. Then we use ALOOCV to provide an optimization algorithm for finding the regularizer in the empirical risk minimization framework. In our numerical experiments, we illustrate the accuracy and efficiency of ALOOCV as well as our proposed framework for the optimization of the regularizer.

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

Apple shares are coming off their longest sell-off in more than three years as escalating attacks from the White House threaten to further erode the company's profit outlook, suggesting the stock's struggles this year are far from over. U.S. President Donald Trump on Friday threatened to levy a 25% tariff on the company's products if it doesn't shift iPhone production to the U.S. Shares fell 3% to end the week, their eighth straight negative session, the longest such sell-off since January 2022. The stock rose 1.7% on Tuesday. Some analysts are skeptical that the tariffs will come to pass, but any movement in this direction will put the company in a position where it either has to absorb the higher costs, weighing on its earnings and margins, or pass along higher prices to consumers, which could erode demand at a time when Apple is already struggling with tepid growth and difficulties with its artificial intelligence offerings.

Many image-to-image translation problems are ambiguous, as a single input image may correspond to multiple possible outputs. In this work, we aim to model a distribution of possible outputs in a conditional generative modeling setting. The ambiguity of the mapping is distilled in a low-dimensional latent vector, which can be randomly sampled at test time. A generator learns to map the given input, combined with this latent code, to the output. We explicitly encourage the connection between output and the latent code to be invertible. This helps prevent a many-to-one mapping from the latent code to the output during training, also known as the problem of mode collapse, and produces more diverse results. We explore several variants of this approach by employing different training objectives, network architectures, and methods of injecting the latent code. Our proposed method encourages bijective consistency between the latent encoding and output modes. We present a systematic comparison of our method and other variants on both perceptual realism and diversity.

Furthermore, it remains a convex function over all individual losses, which can lead to convex optimization problems that can be solved effectively with conventional gradient-based methods.

Evaluating a policy by deploying it in the real world can be risky and costly. Off-policy policy evaluation (OPE) algorithms use historical data collected from running a previous policy to evaluate a new policy, which provides a means for evaluating a policy without requiring it to ever be deployed. Importance sampling is a popular OPE method because it is robust to partial observability and works with continuous states and actions. However, the amount of historical data required by importance sampling can scale exponentially with the horizon of the problem: the number of sequential decisions that are made. We propose using policies over temporally extended actions, called options, and show that combining these policies with importance sampling can significantly improve performance for long-horizon problems. In addition, we can take advantage of special cases that arise due to options-based policies to further improve the performance of importance sampling. We further generalize these special cases to a general covariance testing rule that can be used to decide which weights to drop in an IS estimate, and derive a new IS algorithm called Incremental Importance Sampling that can provide significantly more accurate estimates for a broad class of domains.

The U.S. and its allies across the Atlantic must forge a technology partnership and win the artificial intelligence race even as China makes steady advances, the U.K.'s envoy in Washington said. Ambassador Peter Mandelson warned of the consequences if China continues to get ahead in AI and other key technologies. "They will be able to do things which cascade down not just to their own country but everyone else's across the world," Mandelson said at an event hosted by the Atlantic Council in Washington on Tuesday. "There is nothing I fear more in this world than China winning the race for technological dominance."

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/