Welcome to the fourth edition of the AI Index Report. This year we significantly expanded the amount of data available in the report, worked with a broader set of external organizations to calibrate our data, and deepened our connections with the Stanford Institute for Human-Centered Artificial Intelligence (HAI). The AI Index Report tracks, collates, distills, and visualizes data related to artificial intelligence. Its mission is to provide unbiased, rigorously vetted, and globally sourced data for policymakers, researchers, executives, journalists, and the general public to develop intuitions about the complex field of AI. The report aims to be the most credible and authoritative source for data and insights about AI in the world.

Echo State Networks (ESNs) are a special type of recurrent neural networks (RNNs), in which the input and recurrent connections are traditionally generated randomly, and only the output weights are trained. Despite the recent success of ESNs in various tasks of audio, image and radar recognition, we postulate that a purely random initialization is not the ideal way of initializing ESNs. The aim of this work is to propose an unsupervised initialization of the input connections using the K-Means algorithm on the training data. We show that this initialization performs equivalently or superior than a randomly initialized ESN whilst needing significantly less reservoir neurons (2000 vs. 4000 for spoken digit recognition, and 300 vs. 8000 neurons for f0 extraction) and thus reducing the amount of training time. Furthermore, we discuss that this approach provides the opportunity to estimate the suitable size of the reservoir based on the prior knowledge about the data.

Continuous engineering of autonomous driving functions commonly requires deploying vehicles in road testing to obtain inputs that cause problematic decisions. Although the discovery leads to producing an improved system, it also challenges the foundation of testing using equivalence classes and the associated relative test coverage criterion. In this paper, we propose believed equivalence, where the establishment of an equivalence class is initially based on expert belief and is subject to a set of available test cases having a consistent valuation. Upon a newly encountered test case that breaks the consistency, one may need to refine the established categorization in order to split the originally believed equivalence into two. Finally, we focus on modules implemented using deep neural networks where every category partitions an input over the real domain. We establish new equivalence classes by guiding the new test cases following directions suggested by its k-nearest neighbors, complemented by local robustness testing. The concept is demonstrated in a lane-keeping assist module indicating the potential of our proposed approach.

It is challenging to deal with censored data, where we only have access to the incomplete information of survival time instead of its exact value. Fortunately, under linear predictor assumption, people can obtain guaranteed coverage for the confidence band of survival time using methods like Cox Regression. However, when relaxing the linear assumption with neural networks (e.g., Cox-MLP \citep{katzman2018deepsurv,kvamme2019time}), we lose the guaranteed coverage. To recover the guaranteed coverage without linear assumption, we propose two algorithms based on conformal inference. In the first algorithm \emph{WCCI}, we revisit weighted conformal inference and introduce a new non-conformity score based on partial likelihood. We then propose a two-stage algorithm \emph{T-SCI}, where we run WCCI in the first stage and apply quantile conformal inference to calibrate the results in the second stage. Theoretical analysis shows that T-SCI returns guaranteed coverage under milder assumptions than WCCI. We conduct extensive experiments on synthetic data and real data using different methods, which validate our analysis.

A large number of time series forecasting models including traditional statistical models, machine learning models and more recently deep learning have been proposed in the literature. However, choosing the right model along with good parameter values that performs well on a given data is still challenging. Automatically providing a good set of models to users for a given dataset saves both time and effort from using trial-and-error approaches with a wide variety of available models along with parameter optimization. We present AutoAI for Time Series Forecasting (AutoAI-TS) that provides users with a zero configuration (zero-conf ) system to efficiently train, optimize and choose best forecasting model among various classes of models for the given dataset. With its flexible zero-conf design, AutoAI-TS automatically performs all the data preparation, model creation, parameter optimization, training and model selection for users and provides a trained model that is ready to use. For given data, AutoAI-TS utilizes a wide variety of models including classical statistical models, Machine Learning (ML) models, statistical-ML hybrid models and deep learning models along with various transformations to create forecasting pipelines. It then evaluates and ranks pipelines using the proposed T-Daub mechanism to choose the best pipeline. The paper describe in detail all the technical aspects of AutoAI-TS along with extensive benchmarking on a variety of real world data sets for various use-cases. Benchmark results show that AutoAI-TS, with no manual configuration from the user, automatically trains and selects pipelines that on average outperform existing state-of-the-art time series forecasting toolkits.

A label is a variable to be predicted. In this example, I will predict whether the website visitor will make any transactions and I gave this label the name "purchase". This can be derived from the existing variable "totals.transactions". For simplicity, let's make this prediction a black or white situation, either "purchase" or "no purchase". Since the model training cannot handle string value as the output result, therefore it is necessary to code them into numbers.

We consider stochastic optimization problems where a smooth (and potentially nonconvex) objective is to be minimized using a stochastic first-order oracle. These type of problems arise in many settings from simulation optimization to deep learning. We present Retrospective Approximation (RA) as a universal sequential sample-average approximation (SAA) paradigm where during each iteration $k$, a sample-path approximation problem is implicitly generated using an adapted sample size $M_k$, and solved (with prior solutions as "warm start") to an adapted error tolerance $\epsilon_k$, using a "deterministic method" such as the line search quasi-Newton method. The principal advantage of RA is that decouples optimization from stochastic approximation, allowing the direct adoption of existing deterministic algorithms without modification, thus mitigating the need to redesign algorithms for the stochastic context. A second advantage is the obvious manner in which RA lends itself to parallelization. We identify conditions on $\{M_k, k \geq 1\}$ and $\{\epsilon_k, k\geq 1\}$ that ensure almost sure convergence and convergence in $L_1$-norm, along with optimal iteration and work complexity rates. We illustrate the performance of RA with line-search quasi-Newton on an ill-conditioned least squares problem, as well as an image classification problem using a deep convolutional neural net.

A multi-armed bandit can be considered as a special case We propose a bandit algorithm that explores purely of linear bandits, where the feature vector of each arm is by randomizing its past observations. In particular, a one-hot vector indicating the index of the arm, and the the sufficient optimism in the mean reward estimates parameter vector is a vector of corresponding mean rewards. is achieved by exploiting the variance in Arguably, the most popular and well-studied exploration the past observed rewards. We name the algorithm strategies for solving bandit problems are Thompson sampling Capitalizing On Rewards (CORe). The algorithm (TS) [Thompson, 1933, Agrawal and Goyal, 2013] is general and can be easily applied to different and Optimism in the Face of Uncertainty (OFU) [Auer et al., bandit settings. The main benefit of CORe is that 2002]. TS maintains a posterior distribution over each arm's its exploration is fully data-dependent.

Deep learning has been the engine powering many successes of data science. However, the deep neural network (DNN), as the basic model of deep learning, is often excessively over-parameterized, causing many difficulties in training, prediction and interpretation. We propose a frequentist-like method for learning sparse DNNs and justify its consistency under the Bayesian framework: the proposed method could learn a sparse DNN with at most $O(n/\log(n))$ connections and nice theoretical guarantees such as posterior consistency, variable selection consistency and asymptotically optimal generalization bounds. In particular, we establish posterior consistency for the sparse DNN with a mixture Gaussian prior, show that the structure of the sparse DNN can be consistently determined using a Laplace approximation-based marginal posterior inclusion probability approach, and use Bayesian evidence to elicit sparse DNNs learned by an optimization method such as stochastic gradient descent in multiple runs with different initializations. The proposed method is computationally more efficient than standard Bayesian methods for large-scale sparse DNNs. The numerical results indicate that the proposed method can perform very well for large-scale network compression and high-dimensional nonlinear variable selection, both advancing interpretable machine learning.

We study the problem of predicting as well as the best linear predictor in a bounded Euclidean ball with respect to the squared loss. When only boundedness of the data generating distribution is assumed, we establish that the least squares estimator constrained to a bounded Euclidean ball does not attain the classical $O(d/n)$ excess risk rate, where $d$ is the dimension of the covariates and $n$ is the number of samples. In particular, we construct a bounded distribution such that the constrained least squares estimator incurs an excess risk of order $\Omega(d^{3/2}/n)$ hence refuting a recent conjecture of Ohad Shamir [JMLR 2015]. In contrast, we observe that non-linear predictors can achieve the optimal rate $O(d/n)$ with no assumptions on the distribution of the covariates. We discuss additional distributional assumptions sufficient to guarantee an $O(d/n)$ excess risk rate for the least squares estimator. Among them are certain moment equivalence assumptions often used in the robust statistics literature. While such assumptions are central in the analysis of unbounded and heavy-tailed settings, our work indicates that in some cases, they also rule out unfavorable bounded distributions.