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This paper formulates a general cross validation framework for signal denoising. The general framework is then applied to nonparametric regression methods such as Trend Filtering and Dyadic CART. The resulting cross validated versions are then shown to attain nearly the same rates of convergence as are known for the optimally tuned analogues. There did not exist any previous theoretical analyses of cross validated versions of Trend Filtering or Dyadic CART. To illustrate the generality of the framework we also propose and study cross validated versions of two fundamental estimators; lasso for high dimensional linear regression and singular value thresholding for matrix estimation. Our general framework is inspired by the ideas in Chatterjee and Jafarov (2015) and is potentially applicable to a wide range of estimation methods which use tuning parameters.

This paper proposes a novel graph-based regularized regression estimator - the hierarchical feature regression (HFR) -, which mobilizes insights from the domains of machine learning and graph theory to estimate robust parameters for a linear regression. The estimator constructs a supervised feature graph that decomposes parameters along its edges, adjusting first for common variation and successively incorporating idiosyncratic patterns into the fitting process. The graph structure has the effect of shrinking parameters towards group targets, where the extent of shrinkage is governed by a hyperparamter, and group compositions as well as shrinkage targets are determined endogenously. The method offers rich resources for the visual exploration of the latent effect structure in the data, and demonstrates good predictive accuracy and versatility when compared to a panel of commonly used regularization techniques across a range of empirical and simulated regression tasks.

Metric $k$-center clustering is a fundamental unsupervised learning primitive. Although widely used, this primitive is heavily affected by noise in the data, so that a more sensible variant seeks for the best solution that disregards a given number $z$ of points of the dataset, called outliers. We provide efficient algorithms for this important variant in the streaming model under the sliding window setting, where, at each time step, the dataset to be clustered is the window $W$ of the most recent data items. Our algorithms achieve $O(1)$ approximation and, remarkably, require a working memory linear in $k+z$ and only logarithmic in $|W|$. As a by-product, we show how to estimate the effective diameter of the window $W$, which is a measure of the spread of the window points, disregarding a given fraction of noisy distances. We also provide experimental evidence of the practical viability of our theoretical results.

Non-orthogonal multiple access (NOMA) is considered a key technology for improving the spectral efficiency of fifth-generation (5G) and beyond 5G cellular networks. NOMA is beneficial when the channel vectors of the users are in the same direction, which is not always possible in conventional wireless systems. With the help of a reconfigurable intelligent surface (RIS), the base station can control the directions of the channel vectors of the users. Thus, by combining both technologies, the RIS-assisted NOMA systems are expected to achieve greater improvements in the network throughput. However, ideal phase control at the RIS is unrealizable in practice because of the imperfections in the channel estimations and the hardware limitations. This imperfection in phase control can have a significant impact on the system performance. Motivated by this, in this paper, we consider an RIS-assisted uplink NOMA system in the presence of imperfect phase compensation. We formulate the criterion for pairing the users that achieves minimum required data rates. We propose adaptive user pairing algorithms that maximize spectral or energy efficiency. We then derive various bounds on power allocation factors for the paired users. Through extensive simulation results, we show that the proposed algorithms significantly outperform the state-of-the-art algorithms in terms of spectral and energy efficiency.

One of the reasons that higher order moment portfolio optimization methods are not fully used by practitioners in investment decisions is the complexity that these higher moments create by making the optimization problem nonconvex. Many few methods and theoretical results exists in the literature, but the present paper uses the method of successive convex approximation for the mean-variance-skewness problem.

Gaussian process (GP) regression is a fundamental tool in Bayesian statistics. It is also known as kriging and is the Bayesian counterpart to the frequentist kernel ridge regression. Most of the theoretical work on GP regression has focused on a large-$n$ asymptotics, characterising the behaviour of GP regression as the amount of data increases. Fixed-sample analysis is much more difficult outside of simple cases, such as locations on a regular grid. In this work we perform a fixed-sample analysis that was first studied in the context of approximation theory by Driscoll & Fornberg (2002), called the "flat limit". In flat-limit asymptotics, the goal is to characterise kernel methods as the length-scale of the kernel function tends to infinity, so that kernels appear flat over the range of the data. Surprisingly, this limit is well-defined, and displays interesting behaviour: Driscoll & Fornberg showed that radial basis interpolation converges in the flat limit to polynomial interpolation, if the kernel is Gaussian. Leveraging recent results on the spectral behaviour of kernel matrices in the flat limit, we study the flat limit of Gaussian process regression. Results show that Gaussian process regression tends in the flat limit to (multivariate) polynomial regression, or (polyharmonic) spline regression, depending on the kernel. Importantly, this holds for both the predictive mean and the predictive variance, so that the posterior predictive distributions become equivalent. Our results have practical consequences: for instance, they show that optimal GP predictions in the sense of leave-one-out loss may occur at very large length-scales, which would be invisible to current implementations because of numerical difficulties.

This paper proposes a method for modeling human driver interactions that relies on multi-output gaussian processes. The proposed method is developed as a refinement of the game theoretical hierarchical reasoning approach called "level-k reasoning" which conventionally assigns discrete levels of behaviors to agents. Although it is shown to be an effective modeling tool, the level-k reasoning approach may pose undesired constraints for predicting human decision making due to a limited number (usually 2 or 3) of driver policies it extracts. The proposed approach is put forward to fill this gap in the literature by introducing a continuous domain framework that enables an infinite policy space. By using the approach presented in this paper, more accurate driver models can be obtained, which can then be employed for creating high fidelity simulation platforms for the validation of autonomous vehicle control algorithms. The proposed method is validated on a real traffic dataset and compared with the conventional level-k approach to demonstrate its contributions and implications.

One of the key steps in Neural Architecture Search (NAS) is to estimate the performance of candidate architectures. Existing methods either directly use the validation performance or learn a predictor to estimate the performance. However, these methods can be either computationally expensive or very inaccurate, which may severely affect the search efficiency and performance. Moreover, as it is very difficult to annotate architectures with accurate performance on specific tasks, learning a promising performance predictor is often non-trivial due to the lack of labeled data. In this paper, we argue that it may not be necessary to estimate the absolute performance for NAS. On the contrary, we may need only to understand whether an architecture is better than a baseline one. However, how to exploit this comparison information as the reward and how to well use the limited labeled data remains two great challenges. In this paper, we propose a novel Contrastive Neural Architecture Search (CTNAS) method which performs architecture search by taking the comparison results between architectures as the reward. Specifically, we design and learn a Neural Architecture Comparator (NAC) to compute the probability of candidate architectures being better than a baseline one. Moreover, we present a baseline updating scheme to improve the baseline iteratively in a curriculum learning manner. More critically, we theoretically show that learning NAC is equivalent to optimizing the ranking over architectures. Extensive experiments in three search spaces demonstrate the superiority of our CTNAS over existing methods.

The Q-learning algorithm is known to be affected by the maximization bias, i.e. the systematic overestimation of action values, an important issue that has recently received renewed attention. Double Q-learning has been proposed as an efficient algorithm to mitigate this bias. However, this comes at the price of an underestimation of action values, in addition to increased memory requirements and a slower convergence. In this paper, we introduce a new way to address the maximization bias in the form of a "self-correcting algorithm" for approximating the maximum of an expected value. Our method balances the overestimation of the single estimator used in conventional Q-learning and the underestimation of the double estimator used in Double Q-learning. Applying this strategy to Q-learning results in Self-correcting Q-learning. We show theoretically that this new algorithm enjoys the same convergence guarantees as Q-learning while being more accurate. Empirically, it performs better than Double Q-learning in domains with rewards of high variance, and it even attains faster convergence than Q-learning in domains with rewards of zero or low variance. These advantages transfer to a Deep Q Network implementation that we call Self-correcting DQN and which outperforms regular DQN and Double DQN on several tasks in the Atari 2600 domain.

Click-through rate (CTR) prediction is one of the fundamental tasks for e-commerce search engines. As search becomes more personalized, it is necessary to capture the user interest from rich behavior data. Existing user behavior modeling algorithms develop different attention mechanisms to emphasize query-relevant behaviors and suppress irrelevant ones. Despite being extensively studied, these attentions still suffer from two limitations. First, conventional attentions mostly limit the attention field only to a single user's behaviors, which is not suitable in e-commerce where users often hunt for new demands that are irrelevant to any historical behaviors. Second, these attentions are usually biased towards frequent behaviors, which is unreasonable since high frequency does not necessarily indicate great importance. To tackle the two limitations, we propose a novel attention mechanism, termed Kalman Filtering Attention (KFAtt), that considers the weighted pooling in attention as a maximum a posteriori (MAP) estimation. By incorporating a priori, KFAtt resorts to global statistics when few user behaviors are relevant. Moreover, a frequency capping mechanism is incorporated to correct the bias towards frequent behaviors. Offline experiments on both benchmark and a 10 billion scale real production dataset, together with an Online A/B test, show that KFAtt outperforms all compared state-of-the-arts. KFAtt has been deployed in the ranking system of a leading e commerce website, serving the main traffic of hundreds of millions of active users everyday.