The case-control sampling design serves as a pivotal strategy in mitigating the imbalanced structure observed in binary data. We consider the estimation of a non-parametric logistic model with the case-control data supplemented by external summary information. The incorporation of external summary information ensures the identifiability of the model. We propose a two-step estimation procedure. In the first step, the external information is utilized to estimate the marginal case proportion. In the second step, the estimated proportion is used to construct a weighted objective function for parameter training. A deep neural network architecture is employed for functional approximation. We further derive the non-asymptotic error bound of the proposed estimator. Following this the convergence rate is obtained and is shown to reach the optimal speed of the non-parametric regression estimation. Simulation studies are conducted to evaluate the theoretical findings of the proposed method. A real data example is analyzed for illustration.

There is presently great interest in the abilities of neural networks to mimic "qualitative reasoning" by manipulating neural incodings of symbols. Less work has been performed on using neural networks to process floating point numbers and it is sometimes stated that neural networks are somehow inherently inaccu(cid:173) rate and therefore best suited for "fuzzy" qualitative reasoning. Nevertheless, the potential speed of massively parallel operations make neural net "number crunching" an interesting topic to explore. In this paper we discuss some of our work in which we demonstrate that for certain applications neural networks can achieve significantly higher numerical accuracy than more conventional tech(cid:173) niques. In particular, prediction of future values of a chaotic time series can be performed with exceptionally high accuracy.

In this article, we will try to understand where On-Policy learning, Off-policy learning and offline learning algorithms fundamentally differ. Though there is a fair amount of intimidating jargon in reinforcement learning theory, these are just based on simple ideas. Reinforcement Learning is a subfield of machine learning that teaches an agent how to choose an action from its action space. It interacts with an environment, in order to maximize rewards over time. Complex enough? let's break this definition for better understanding.