Tag Archives: Adaptive Data Analysis

Estimating the Impact of Training Data with Reinforcement Learning

Recent work suggests that not all data samples are equally useful for training, particularly for deep neural networks (DNNs). Indeed, if a dataset contains low-quality or incorrectly labeled data, one can often improve performance by removing a significant portion of training samples. Moreover, in cases where there is a mismatch between the train and test datasets (e.g., due to difference in train and test location or time), one can also achieve higher performance by carefully restricting samples in the training set to those most relevant for the test scenario. Because of the ubiquity of these scenarios, accurately quantifying the values of training samples has great potential for improving model performance on real-world datasets.

Top: Examples of low-quality samples (noisy/crowd-sourced); Bottom: Examples of a train and test mismatch.

In addition to improving model performance, assigning a quality value to individual data can also enable new use cases. It can be used to suggest better practices for data collection, e.g., what kinds of additional data would benefit the most, and can be used to construct large-scale training datasets more efficiently, e.g., by web searching using the labels as keywords and filtering out less valuable data.

In “Data Valuation Using Deep Reinforcement Learning”, accepted at ICML 2020, we address the challenge of quantifying the value of training data using a novel approach based on meta-learning. Our method integrates data valuation into the training procedure of a predictor model that learns to recognize samples that are more valuable for the given task, improving both predictor and data valuation performance. We have also launched four AI Hub Notebooks that exemplify the use cases of DVRL and are designed to be conveniently adapted to other tasks and datasets, such as domain adaptationcorrupted sample discovery and robust learningtransfer learning on image data and data valuation.

Quantifying the Value of Data
Not all data are equal for a given ML model — some have greater relevance for the task at hand or are more rich in informative content than others. So how does one evaluate the value of a single datum? At the granularity of a full dataset, it is straightforward; one can simply train a model on the entire dataset and use its performance on a test set as its value. However, estimating the value of a single datum is far more difficult, especially for complex models that rely on large-scale datasets, because it is computationally infeasible to re-train and re-evaluate a model on all possible subsets.

To tackle this, researchers have explored permutation-based methods (e.g., influence functions), and game theory-based methods (e.g., data Shapley). However, even the best current methods are far from being computationally feasible for large datasets and complex models, and their data valuation performance is limited. Concurrently, meta learning-based adaptive weight assignment approaches have been developed to estimate the weight values using a meta-objective. But rather than prioritizing learning from high value data samples, their data value mapping is typically based on gradient descent learning or other heuristic approaches that alter the conventional predictor model training dynamics, which can result in performance changes that are unrelated to the value of individual data points.

Data Valuation Using Reinforcement Learning (DVRL)
To infer the data values, we propose a data value estimator (DVE) that estimates data values and selects the most valuable samples to train the predictor model. This selection operation is fundamentally non-differentiable and thus conventional gradient descent-based methods cannot be used. Instead, we propose to use reinforcement learning (RL) such that the supervision of the DVE is based on a reward that quantifies the predictor performance on a small (but clean) validation set. The reward guides the optimization of the policy towards the action of optimal data valuation, given the state and input samples. Here, we treat the predictor model learning and evaluation framework as the environment, a novel application scenario of RL-assisted machine learning.

Training with Data Value Estimation using Reinforcement Learning (DVRL). When training the data value estimator with an accuracy reward, the most valuable samples (denoted with green dots) are used more and more, whereas the least valuable samples (red dots) are used less frequently.

We evaluate the data value estimation quality of DVRL on multiple types of datasets and use cases.

  • Model performance after removing high/low value samples
    Removing low value samples from the training dataset can improve the predictor model performance, especially in the cases where the training dataset contains corrupted samples. On the other hand, removing high value samples, especially if the dataset is small, decreases the performance significantly. Overall, the performance after removing high/low value samples is a strong indicator for the quality of data valuation.
    Accuracy with the removal of most and least valuable samples, where 20% of the labels are noisy by design. By removing such noisy labels as the least valuable samples, a high-quality data valuation method achieves better accuracy. We demonstrate that DVRL outperforms other methods significantly from this perspective.
    DVRL shows the fastest performance degradation after removing the most important samples and the slowest performance degradation after removing the least important samples in most cases, underlining the superiority of DVRL in identifying noisy labels compared to competing methods (Leave-One-Out and Data Shapley).

  • Robust learning with noisy labels
    We consider how reliably DVRL can learn with noisy data in an end-to-end way, without removing the low-value samples. Ideally, noisy samples should get low data values as DVRL converges and a high performance model would be returned.
    Robust learning with noisy labels. Test accuracy for ResNet-32 and WideResNet-28-10 on CIFAR-10 and CIFAR-100 datasets with 40% of uniform random noise on labels. DVRL outperforms other popular methods that are based on meta-learning.
    We show state-of-the-art results with DVRL in minimizing the impact of noisy labels. These also demonstrate that DVRL can scale to complex models and large-scale datasets.

  • Domain adaptation
    We consider the scenario where the training dataset comes from a substantially different distribution from the validation and testing datasets. Data valuation is expected to be beneficial for this task by selecting the samples from the training dataset that best match the distribution of the validation dataset. We focus on the three cases: (1) a training set based on image search results (low-quality web-scraped) applied to the task of predicting skin lesion classification using HAM 10000 data (high-quality medical); (2) an MNIST training set for a digit recognition task on USPS data (different visual domain); (3) e-mail spam data to detect spam applied to an SMS dataset (different task). DVRL yields significant improvements for domain adaptation, by jointly optimizing the data valuator and corresponding predictor model.

We propose a novel meta learning framework for data valuation which determines how likely each training sample will be used in training of the predictor model. Unlike previous works, our method integrates data valuation into the training procedure of the predictor model, allowing the predictor and DVE to improve each other's performance. We model this data value estimation task using a DNN trained through RL with a reward obtained from a small validation set that represents the target task performance. In a computationally-efficient way, DVRL can provide high quality ranking of training data that is useful for domain adaptation, corrupted sample discovery and robust learning. We show that DVRL significantly outperforms alternative methods on diverse types of tasks and datasets.

We gratefully acknowledge the contributions of Tomas Pfister.

Source: Google AI Blog

The reusable holdout: Preserving validity in adaptive data analysis

Machine learning and statistical analysis play an important role at the forefront of scientific and technological progress. But with all data analysis, there is a danger that findings observed in a particular sample do not generalize to the underlying population from which the data were drawn. A popular XKCD cartoon illustrates that if you test sufficiently many different colors of jelly beans for correlation with acne, you will eventually find one color that correlates with acne at a p-value below the infamous 0.05 significance level.
Image credit: XKCD
Unfortunately, the problem of false discovery is even more delicate than the cartoon suggests. Correcting reported p-values for a fixed number of multiple tests is a fairly well understood topic in statistics. A simple approach is to multiply each p-value by the number of tests, but there are more sophisticated tools. However, almost all existing approaches to ensuring the validity of statistical inferences assume that the analyst performs a fixed procedure chosen before the data are examined. For example, “test all 20 flavors of jelly beans”. In practice, however, the analyst is informed by data exploration, as well as the results of previous analyses. How did the scientist choose to study acne and jelly beans in the first place? Often such choices are influenced by previous interactions with the same data. This adaptive behavior of the analyst leads to an increased risk of spurious discoveries that are neither prevented nor detected by standard approaches. Each adaptive choice the analyst makes multiplies the number of possible analyses that could possibly follow; it is often difficult or impossible to describe and analyze the exact experimental setup ahead of time.

In The Reusable Holdout: Preserving Validity in Adaptive Data Analysis, a joint work with Cynthia Dwork (Microsoft Research), Vitaly Feldman (IBM Almaden Research Center), Toniann Pitassi (University of Toronto), Omer Reingold (Samsung Research America) and Aaron Roth (University of Pennsylvania), to appear in Science tomorrow, we present a new methodology for navigating the challenges of adaptivity. A central application of our general approach is the reusable holdout mechanism that allows the analyst to safely validate the results of many adaptively chosen analyses without the need to collect costly fresh data each time.

The curse of adaptivity

A beautiful example of how false discovery arises as a result of adaptivity is Freedman’s paradox. Suppose that we want to build a model that explains “systolic blood pressure” in terms of hundreds of variables quantifying the intake of various kinds of food. In order to reduce the number of variables and simplify our task, we first select some promising looking variables, for example, those that have a positive correlation with the response variable (systolic blood pressure). We then fit a linear regression model on the selected variables. To measure the goodness of our model fit, we crank out a standard F-test from our favorite statistics textbook and report the resulting p-value.
Inference after selection: We first select a subset of the variables based on a data-dependent criterion and then fit a linear model on the selected variables.
Freedman showed that the reported p-value is highly misleading - even if the data were completely random with no correlation whatsoever between the response variable and the data points, we’d likely observe a significant p-value! The bias stems from the fact that we selected a subset of the variables adaptively based on the data, but we never account for this fact. There is a huge number of possible subsets of variables that we selected from. The mere fact that we chose one test over the other by peeking at the data creates a selection bias that invalidates the assumptions underlying the F-test.

Freedman’s paradox bears an important lesson. Significance levels of standard procedures do not capture the vast number of analyses one can choose to carry out or to omit. For this reason, adaptivity is one of the primary explanations of why research findings are frequently false as was argued by Gelman and Loken who aptly refer to adaptivity as “garden of the forking paths”.

Machine learning competitions and holdout sets

Adaptivity is not just an issue with p-values in the empirical sciences. It affects other domains of data science just as well. Machine learning competitions are a perfect example. Competitions have become an extremely popular format for solving prediction and classification problems of all sorts.

Each team in the competition has full access to a publicly available training set which they use to build a predictive model for a certain task such as image classification. Competitors can repeatedly submit a model and see how the model performs on a fixed holdout data set not available to them. The central component of any competition is the public leaderboard which ranks all teams according to the prediction accuracy of their best model so far on the holdout. Every time a team makes a submission they observe the score of their model on the same holdout data. This methodology is inspired by the classic holdout method for validating the performance of a predictive model.
Ideally, the holdout score gives an accurate estimate of the true performance of the model on the underlying distribution from which the data were drawn. However, this is only the case when the model is independent of the holdout data! In contrast, in a competition the model generally incorporates previously observed feedback from the holdout set. Competitors work adaptively and iteratively with the feedback they receive. An improved score for one submission might convince the team to tweak their current approach, while a lower score might cause them to try out a different strategy. But the moment a team modifies their model based on a previously observed holdout score, they create a dependency between the model and the holdout data that invalidates the assumption of the classic holdout method. As a result, competitors may begin to overfit to the holdout data that supports the leaderboard. This means that their score on the public leaderboard continues to improve, while the true performance of the model does not. In fact, unreliable leaderboards are a widely observed phenomenon in machine learning competitions.

Reusable holdout sets

A standard proposal for coping with adaptivity is simply to discourage it. In the empirical sciences, this proposal is known as pre-registration and requires the researcher to specify the exact experimental setup ahead of time. While possible in some simple cases, it is in general too restrictive as it runs counter to today’s complex data analysis workflows.

Rather than limiting the analyst, our approach provides means of reliably verifying the results of an arbitrary adaptive data analysis. The key tool for doing so is what we call the reusable holdout method. As with the classic holdout method discussed above, the analyst is given unfettered access to the training data. What changes is that there is a new algorithm in charge of evaluating statistics on the holdout set. This algorithm ensures that the holdout set maintains the essential guarantees of fresh data over the course of many estimation steps.
The limit of the method is determined by the size of the holdout set - the number of times that the holdout set may be used grows roughly as the square of the number of collected data points in the holdout, as our theory shows.

Armed with the reusable holdout, the analyst is free to explore the training data and verify tentative conclusions on the holdout set. It is now entirely safe to use any information provided by the holdout algorithm in the choice of new analyses to carry out, or the tweaking of existing models and parameters.

A general methodology

The reusable holdout is only one instance of a broader methodology that is, perhaps surprisingly, based on differential privacy—a notion of privacy preservation in data analysis. At its core, differential privacy is a notion of stability requiring that any single sample should not influence the outcome of the analysis significantly.
Example of a stable learning algorithm: Deletion of any single data point does not affect the accuracy of the classifier much.
A beautiful line of work in machine learning shows that various notions of stability imply generalization. That is any sample estimate computed by a stable algorithm (such as the prediction accuracy of a model on a sample) must be close to what we would observe on fresh data.

What sets differential privacy apart from other stability notions is that it is preserved by adaptive composition. Combining multiple algorithms that each preserve differential privacy yields a new algorithm that also satisfies differential privacy albeit at some quantitative loss in the stability guarantee. This is true even if the output of one algorithm influences the choice of the next. This strong adaptive composition property is what makes differential privacy an excellent stability notion for adaptive data analysis.

In a nutshell, the reusable holdout mechanism is simply this: access the holdout set only through a suitable differentially private algorithm. It is important to note, however, that the user does not need to understand differential privacy to use our method. The user interface of the reusable holdout is the same as that of the widely used classical method.

Reliable benchmarks

A closely related work with Avrim Blum dives deeper into the problem of maintaining a reliable leaderboard in machine learning competitions (see this blog post for more background). While the reusable holdout could directly be used for this purpose, it turns out that a variant of the reusable holdout, we call the Ladder algorithm, provides even better accuracy.

This method is not just useful for machine learning competitions, since there are many problems that are roughly equivalent to that of maintaining an accurate leaderboard in a competition. Consider, for example, a performance benchmark that a company uses to test improvements to a system internally before deploying them in a production system. As the benchmark data set is used repeatedly and adaptively for tasks such as model selection, hyper-parameter search and testing, there is a danger that eventually the benchmark becomes unreliable.


Modern data analysis is inherently an adaptive process. Attempts to limit what data scientists will do in practice are ill-fated. Instead we should create tools that respect the usual workflow of data science while at the same time increasing the reliability of data driven insights. It is our goal to continue exploring techniques that can help to create more reliable validation techniques and benchmarks that track true performance more accurately than existing methods.