In most practical applications such as recommendation systems, display advertising, and so forth, the collected data often contains missing values and those missing values are generally missing-not-at-random, which deteriorates the prediction performance of models. Some existing estimators and regularizers attempt to achieve unbiased estimation to improve the predictive performance. However, variances and generalization bound of these methods are generally unbounded when the propensity scores tend to zero, compromising their stability and robustness. In this paper, we first theoretically reveal that limitations of regularization techniques. Besides, we further illustrate that, for more general estimators, unbiasedness will inevitably lead to unbounded variance.

Some existing estimators and regularizers attempt to achieve unbiased estimation to improve the predictive performance.

In recent years, a large number of algorithms for label integration and noise correction have been proposed to infer the unknown true labels of instances in crowdsourcing.

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Scarcity of labeled training data remains the long pole in the tent for building performant language technology and generative AI models. Transformer models -- particularly LLMs -- are increasingly being used to mitigate the data scarcity problem via synthetic data generation. However, because the models are black boxes, the properties of the synthetic data are difficult to predict. In practice it is common for language technology engineers to 'fiddle' with the LLM temperature setting and hope that what comes out the other end improves the downstream model. Faced with this uncertainty, here we propose Data Kernel Perspective Space (DKPS) to provide the foundation for mathematical analysis yielding concrete statistical guarantees for the quality of the outputs of transformer models. We first show the mathematical derivation of DKPS and how it provides performance guarantees. Next we show how DKPS performance guarantees can elucidate performance of a downstream task, such as neural machine translation models or LLMs trained using Contrastive Preference Optimization (CPO). Limitations of the current work and future research are also discussed.

Online A/B tests have become increasingly popular and important for social platforms. However, accurately estimating the global average treatment effect (GATE) has proven to be challenging due to network interference, which violates the Stable Unit Treatment Value Assumption (SUTVA) and poses great challenge to experimental design. Existing network experimental design research was mostly based on the unbiased Horvitz-Thompson (HT) estimator with substantial data trimming to ensure unbiasedness at the price of high resultant estimation variance. In this paper, we strive to balance the bias and variance in designing randomized network experiments. Under a potential outcome model with 1-hop interference, we derive the bias and variance of the standard HT estimator and reveal their relation to the network topological structure and the covariance of the treatment assignment vector. We then propose to formulate the experimental design problem as to optimize the covariance matrix of the treatment assignment vector to achieve the bias and variance balance by minimizing the mean squared error (MSE) of the estimator. An efficient projected gradient descent algorithm is presented to the implement of the desired randomization scheme. Finally, we carry out extensive simulation studies to demonstrate the advantages of our proposed method over other existing methods in many settings, with different levels of model misspecification.

Gradient-based methods for optimisation of objectives in stochastic settings with unknown or intractable dynamics require estimators of derivatives. We derive an objective that, under automatic differentiation, produces low-variance unbiased estimators of derivatives at any order. Our objective is compatible with arbitrary advantage estimators, which allows the control of the bias and variance of any-order derivatives when using function approximation. Furthermore, we propose a method to trade off bias and variance of higher order derivatives by discounting the impact of more distant causal dependencies. We demonstrate the correctness and utility of our estimator in analytically tractable MDPs and in meta-reinforcement-learning for continuous control.

Perception, in theoretical neuroscience, has been modeled as the encoding of external stimuli into internal signals, which are then decoded. The Bayesian mean is an important decoder, as it is optimal for purposes of both estimation and discrimination. We present widely-applicable approximations to the bias and to the variance of the Bayesian mean, obtained under the minimal and biologically-relevant assumption that the encoding results from a series of independent, though not necessarily identically-distributed, signals. Simulations substantiate the accuracy of our approximations in the small-noise regime. The bias of the Bayesian mean comprises two components: one driven by the prior, and one driven by the precision of the encoding.