Whole-brain neural connectivity data are now available from viral tracing experiments, which reveal the connections between a source injection site and elsewhere in the brain.

Most online optimization algorithms focus on one of two things: performing well in adversarial settings by adapting to unknown data parameters (such as Lipschitz constants), typically achieving $O(\sqrt{T})$ regret, or performing well in stochastic settings where they can leverage some structure in the losses (such as strong convexity), typically achieving $O(\log(T))$ regret. Algorithms that focus on the former problem hitherto achieved $O(\sqrt{T})$ in the stochastic setting rather than $O(\log(T))$. Here we introduce an online optimization algorithm that achieves $O(\log^4(T))$ regret in a wide class of stochastic settings while gracefully degrading to the optimal $O(\sqrt{T})$ regret in adversarial settings (up to logarithmic factors). Our algorithm does not require any prior knowledge about the data or tuning of parameters to achieve superior performance.

Predicated on the increasing abundance of electronic health records, we investigate the problem of inferring individualized treatment effects using observational data. Stemming from the potential outcomes model, we propose a novel multi-task learning framework in which factual and counterfactual outcomes are modeled as the outputs of a function in a vector-valued reproducing kernel Hilbert space (vvRKHS). We develop a nonparametric Bayesian method for learning the treatment effects using a multi-task Gaussian process (GP) with a linear coregionalization kernel as a prior over the vvRKHS. The Bayesian approach allows us to compute individualized measures of confidence in our estimates via pointwise credible intervals, which are crucial for realizing the full potential of precision medicine. The impact of selection bias is alleviated via a risk-based empirical Bayes method for adapting the multi-task GP prior, which jointly minimizes the empirical error in factual outcomes and the uncertainty in (unobserved) counterfactual outcomes. We conduct experiments on observational datasets for an interventional social program applied to premature infants, and a left ventricular assist device applied to cardiac patients wait-listed for a heart transplant. In both experiments, we show that our method significantly outperforms the state-of-the-art.

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

The goal of minimizing misclassification error on a training set is often just one of several real-world goals that might be defined on different datasets. For example, one may require a classifier to also make positive predictions at some specified rate for some subpopulation (fairness), or to achieve a specified empirical recall. Other real-world goals include reducing churn with respect to a previously deployed model, or stabilizing online training. In this paper we propose handling multiple goals on multiple datasets by training with dataset constraints, using the ramp penalty to accurately quantify costs, and present an efficient algorithm to approximately optimize the resulting non-convex constrained optimization problem. Experiments on both benchmark and real-world industry datasets demonstrate the effectiveness of our approach.

We consider online learning algorithms that guarantee worst-case regret rates in adversarial environments (so they can be deployed safely and will perform robustly), yet adapt optimally to favorable stochastic environments (so they will perform well in a variety of settings of practical importance). We quantify the friendliness of stochastic environments by means of the well-known Bernstein (a.k.a.

The cornerstone of modern math wouldn't be possible without the Hindu-Arabic numerical system. Breakthroughs, discoveries, and DIY tips sent every weekday. Most people know about Pi Day (3/14), but there are even rarer days on the calendar like Pythagorean Triple Square Day (9/16/25). The poetry of mathematics manifests everywhere in nature, but few numerical patterns are more common than the Fibonacci Sequence . First described in 1202 by mathematician Italian Leonardo Bonacci (Fibonacci is a shortening of or "son of Bonacci"), the concept involves adding 1 and 1 together, then doing the same for every successive pair of numbers.

Inference using deep neural networks is often outsourced to the cloud since it is a computationally demanding task.

Stochastic gradient methods for machine learning and optimization problems are usually analyzed assuming data points are sampled replacement. In contrast, sampling replacement is far less understood, yet in practice it is very common, often easier to implement, and usually performs better. In this paper, we provide competitive convergence guarantees for without-replacement sampling under several scenarios, focusing on the natural regime of few passes over the data. Moreover, we describe a useful application of these results in the context of distributed optimization with randomly-partitioned data, yielding a nearly-optimal algorithm for regularized least squares (in terms of both communication complexity and runtime complexity) under broad parameter regimes. Our proof techniques combine ideas from stochastic optimization, adversarial online learning and transductive learning theory, and can potentially be applied to other stochastic optimization and learning problems.

We present a novel deep recurrent neural network architecture that learns to build implicit plans in an end-to-end manner purely by interacting with an environment in reinforcement learning setting. The network builds an internal plan, which is continuously updated upon observation of the next input from the environment. It can also partition this internal representation into contiguous sub-sequences by learning for how long the plan can be committed to -- i.e. followed without replaning. Combining these properties, the proposed model, dubbed STRategic Attentive Writer (STRAW) can learn high-level, temporally abstracted macro-actions of varying lengths that are solely learnt from data without any prior information. These macro-actions enable both structured exploration and economic computation. We experimentally demonstrate that STRAW delivers strong improvements on several ATARI games by employing temporally extended planning strategies (e.g.