The goal has been to construct a supervised artificial neural network that learns incrementally an unknown mapping. As a result a network con(cid:173) sisting of a combination of ART2 and backpropagation is proposed and is called an "ART2/BP" network. The ART2 network is used to build and focus a supervised backpropagation network. The ART2/BP network has the advantage of being able to dynamically expand itself in response to input patterns containing new information. Simulation results show that the ART2/BP network outperforms a classical maximum likelihood method for the estimation of a discrete dynamic and nonlinear transfer function.

Long before the recent popularity of instrumental variables in modern machine learning causal inference and biostatistics, the instrumental variables technique has been widely used in economics. For instance, instrumental variables regressions are frequently used to account for omitted variables, mis-measured regressors, endogeneity in simultaneous equations and other complex situations in observational data. In economics and other social sciences, as well as in medical research, it is very difficult to estimate causal effects using observational data sets alone. When treatment assignment is not randomized, it is generally impossible to discern between the causal effect of treatments and spurious correlations that are induced by unobserved factors. Instrumental variables are commonly used to provide exogenous variation that is associated with the treatment status, but not with the outcome variable (beyond its direct effect on the treatments). To avoid mis-specification of parametric functional forms, the nonparametric instrumental variables regressions (NPIV) have gained popularity in econometrics and modern causal inference in statistics and machine learning.

Single Photon Emission Computed Tomography (SPECT) imaging is a valu able diagnostic tool that is frequently used to detect the presence of tumors ins ide a patient's body. The idea behind SPECT imaging can be described very briefly in the following m anner: A small amount of radioactive tracer attached to some nutrient is injecte d in the patient's body. After a brief interlude (ranging from a few minutes to a few hours), a SPECT scanner is used to measure the radioactive emissions from the body in a range o f directions by moving the scanner around the body. Along each line, the data represent s the intensity of emissions from a point along that line. This data can be mathematically interpret ed as an attenuated Radon transform. From the attenuated Radon transform data, one then tries to image the inside of the patient's body to locate the presence of tumors. If on e makes the simplifying assumption that the attenuation is constant, then the attenuat ed Radon transform reduces to the case of what is known as the exponential Radon transform. We point the interested reader to [19] and [31] for a more detailed overview. In the setting of the current article, our focus of investigation is t he estimation of a function from its stochastic (i.e.

While standard estimation assumes that all datapoints are from probability distribution of the same fixed parameters $\theta$, we will focus on maximum likelihood (ML) adaptive estimation for nonstationary time series: separately estimating parameters $\theta_T$ for each time $T$ based on the earlier values $(x_t)_{t

Algorithms often carry out equally many computations for "easy" and "hard" problem instances. In particular, algorithms for finding nearest neighbors typically have the same running time regardless of the particular problem instance. In this paper, we consider the approximate k-nearest-neighbor problem, which is the problem of finding a subset of O(k) points in a given set of points that contains the set of k nearest neighbors of a given query point. We propose an algorithm based on adaptively estimating the distances, and show that it is essentially optimal out of algorithms that are only allowed to adaptively estimate distances. We then demonstrate both theoretically and experimentally that the algorithm can achieve significant speedups relative to the naive method.

The multi-armed bandit (MAB) problem is a classic example of the exploration-exploitation dilemma. It is concerned with maximising the total rewards for a gambler by sequentially pulling an arm from a multi-armed slot machine where each arm is associated with a reward distribution. In static MABs, the reward distributions do not change over time, while in dynamic MABs, each arm's reward distribution can change, and the optimal arm can switch over time. Motivated by many real applications where rewards are binary counts, we focus on dynamic Bernoulli bandits. Standard methods like $\epsilon$-Greedy and Upper Confidence Bound (UCB), which rely on the sample mean estimator, often fail to track the changes in underlying reward for dynamic problems. In this paper, we overcome the shortcoming of slow response to change by deploying adaptive estimation in the standard methods and propose a new family of algorithms, which are adaptive versions of $\epsilon$-Greedy, UCB, and Thompson sampling. These new methods are simple and easy to implement. Moreover, they do not require any prior knowledge about the data, which is important for real applications. We examine the new algorithms numerically in different scenarios and find out that the results show solid improvements of our algorithms in dynamic environments.

We study the adaptive estimation of copula correlation matrix $\Sigma$ for the semi-parametric elliptical copula model. In this context, the correlations are connected to Kendall's tau through a sine function transformation. Hence, a natural estimate for $\Sigma$ is the plug-in estimator $\hat{\Sigma}$ with Kendall's tau statistic. We first obtain a sharp bound on the operator norm of $\hat{\Sigma}-\Sigma$. Then we study a factor model of $\Sigma$, for which we propose a refined estimator $\widetilde{\Sigma}$ by fitting a low-rank matrix plus a diagonal matrix to $\hat{\Sigma}$ using least squares with a nuclear norm penalty on the low-rank matrix. The bound on the operator norm of $\hat{\Sigma}-\Sigma$ serves to scale the penalty term, and we obtain finite sample oracle inequalities for $\widetilde{\Sigma}$. We also consider an elementary factor copula model of $\Sigma$, for which we propose closed-form estimators. All of our estimation procedures are entirely data-driven.

The goal has been to construct a supervised artificial neural network that learns incrementally an unknown mapping. As a result a network consisting ofa combination of ART2 and backpropagation is proposed and is called an "ART2/BP" network. The ART2 network is used to build and focus a supervised backpropagation network. The ART2/BP network has the advantage of being able to dynamically expand itself in response to input patterns containing new information. Simulation results show that the ART2/BP network outperforms a classical maximum likelihood method for the estimation of a discrete dynamic and nonlinear transfer function.

The goal has been to construct a supervised artificial neural network that learns incrementally an unknown mapping. As a result a network consisting of a combination of ART2 and backpropagation is proposed and is called an "ART2/BP" network. The ART2 network is used to build and focus a supervised backpropagation network. The ART2/BP network has the advantage of being able to dynamically expand itself in response to input patterns containing new information. Simulation results show that the ART2/BP network outperforms a classical maximum likelihood method for the estimation of a discrete dynamic and nonlinear transfer function.

The goal has been to construct a supervised artificial neural network that learns incrementally an unknown mapping. As a result a network consisting of a combination of ART2 and backpropagation is proposed and is called an "ART2/BP" network. The ART2 network is used to build and focus a supervised backpropagation network. The ART2/BP network has the advantage of being able to dynamically expand itself in response to input patterns containing new information. Simulation results show that the ART2/BP network outperforms a classical maximum likelihood method for the estimation of a discrete dynamic and nonlinear transfer function.