We advocate for a practical Maximum Likelihood Estimation (MLE) approach for regression and forecasting, as an alternative to the typical approach of Empirical Risk Minimization (ERM) for a specific target metric. This approach is better suited to capture inductive biases such as prior domain knowledge in datasets, and can output post-hoc estimators at inference time that can optimize different types of target metrics. We present theoretical results to demonstrate that our approach is always competitive with any estimator for the target metric under some general conditions, and in many practical settings (such as Poisson Regression) can actually be much superior to ERM. We demonstrate empirically that our method instantiated with a well-designed general purpose mixture likelihood family can obtain superior performance over ERM for a variety of tasks across time-series forecasting and regression datasets with different data distributions.

翻译：我们主张对回归和预测采用实际的最大可能性估计(MLE)方法,作为特定指标指标衡量标准典型的 " 经验风险最小化(ERM) " (EMM)方法的替代方法,这种方法更适合捕捉进感性偏差,如数据集中先前的域知识,并可在推论时间输出后热测算器,以优化不同类型的目标指标。我们提出理论结果,以证明我们的方法总是与某些一般条件下目标指标的估测器具有竞争力,在许多实际环境中(如Poisson Regression),实际上可能比机构风险管理高得多。 我们从经验上表明,我们的方法与精心设计的通用组合组合,可能家族在不同数据分布的时间序列预测和回归数据集中获得优于机构风险管理的各种任务。