LLM 평가에 통계 적용

Applying Statistics to LLM Evaluations An overview of useful statistics for building and interpreting LLM evaluations... Research on large language models (LLMs) is empirically driven. For this reason, model evaluations play a pivotal role in the field’s progress. We improve models by making changes, evaluating them, and iterating. Despite their foundational role, however, evaluations are usually handled in a naive manner. In most cases, we just test a model’s performance over a finite evaluation dataset and directly compare performance metrics to those of other models with no consideration for whether these results are statistically significant or not. Such an approach leads to incorrect or misleading interpretations of evaluation results. As researchers, we want to avoid mistaking noise for progress and instead equip ourselves with the statistical tools needed to run informative model evaluations. “Language models are measured in the literature by evaluations, or evals. Evals are commonly run and reported with a highest number is best mentality; industry practice is to highlight a state-of-the-art result in bold, but not necessarily to test that result for any kind of statistical significance.” - from [1] In this overview, we will build a statistical foundation for LLM evaluations from the ground up. To begin, we will review basic statistical ideas with a practical focus on the topics that are most useful for model evaluations. We will then take a deeper look at how these ideas can be directly used to interpret LLM evaluation results in an uncertainty-aware manner. Specifically, we will cover a set of statistical best practices for model evaluation and implement each of them to show how they can be concretely applied. Although it may seem daunting, taking a statistically grounded approach to model evaluation is not especially difficult and can help us make faster progress by avoiding spurious results. Basic Statistics for LLM Evaluations In order to develop a statistical framework for LLM evaluations, we need to first learn about the fundamental tools from statistics that can be used to create such a framework. This section will cover a selection of topics related to the properties of random variables, such as computing the mean or variance and constructing a confidence interval. After covering the fundamentals, we learn how these ideas can be applied to properly analyze LLM evaluation results in the next section. Random Variables and Estimators A random variable X is defined as a quantity that has a value dependent upon chance. We can take several independent samples from the distribution {x_1, x_2, …, x_n} , and the values of these observations will be sampled from the distribution of X (i.e., x_i ~ X ). We define the mean (or average) of this random variable via the expectation, which can be computed in a continuous or discrete fashion as shown in the figure below. Additionally, we can compute a sample mean by averaging the values of n observations sampled from the distribution. Formally, the lower case letters x_i represent concrete values sampled from a distribution, while upper case letter X_i denotes the i -th random variable in our sample—this is a notational detail, but it’s worth covering to avoid confusion. For example, if we evaluate our LLM on n questions, X_i is a random variable that represents the distribution of possible scores for question i1 , while x_i is an actual evaluation score observed for a single evaluation run. We can also define the sample mean in terms of random variables as shown in the equation below. We use an uppercase X̄ in this case because we are defining a random variable. The distribution of our random variable X also has variance Var(X) , which describes how “spread out” the distribution is around the mean. In this overview, we will assume that this variance is finite (i.e., less than infinity). If we have a distribution with high variance, then samples taken from this distribution will be more spread out around the mean and vice versa; see below for an illustration. The expression for Var(X) is provided below. Similarly to the sample mean, we can also estimate variance using a fixed set of samples from our distribution X —this is how the variance is usually computed in practical settings. We can also compute the standard deviation σ by taking the square root of the variance. The variance and standard deviation describe the variability of individual samples from X . While variance measures the variability of a single random variable X , covariance measures how two random variables X and Y vary together. Intuitively, if these variables vary in the same direction (e.g., they are both above or below their means at the same time), then their covariance will be positive and vice versa. A covariance near zero indicates there is no clear relationship between X and Y . We can also compute a sample covariance similarly to the sample variance shown above. Expressions for cova