How Much is Unseen Depends Chiefly on Information About the Seen

It might seem counter-intuitive at first: We find that, in expectation, the proportion of data points in an unknown population-that belong to classes that do not appear in the training data-is almost entirely determined by the number $f_k$ of classes that do appear in the training data the same number of times. While in theory we show that the difference of the induced estimator decays exponentially in the size of the sample, in practice the high variance prevents us from using it directly for an estimator of the sample coverage. However, our precise characterization of the dependency between $f_k$'s induces a large search space of different representations of the expected value, which can be deterministically instantiated as estimators. Hence, we turn to optimization and develop a genetic algorithm that, given only the sample, searches for an estimator with minimal mean-squared error (MSE). In our experiments, our genetic algorithm discovers estimators that have a substantially smaller MSE than the state-of-the-art Good-Turing estimator. This holds for over 96% of runs when there are at least as many samples as classes. Our estimators' MSE is roughly 80% of the Good-Turing estimator's.

Limits of Machine Learning for Automatic Vulnerability Detection

Recent results of machine learning for automatic vulnerability detection have been very promising indeed: Given only the source code of a function $f$, models trained by machine learning techniques can decide if $f$ contains a security flaw with up to 70% accuracy. But how do we know that these results are general and not specific to the datasets? To study this question, researchers proposed to amplify the testing set by injecting semantic preserving changes and found that the model's accuracy significantly drops. In other words, the model uses some unrelated features during classification. In order to increase the robustness of the model, researchers proposed to train on amplified training data, and indeed model accuracy increased to previous levels. In this paper, we replicate and continue this investigation, and provide an actionable model benchmarking methodology to help researchers better evaluate advances in machine learning for vulnerability detection. Specifically, we propose (i) a cross validation algorithm, where a semantic preserving transformation is applied during the amplification of either the training set or the testing set, and (ii) the amplification of the testing set with code snippets where the vulnerabilities are fixed. Using 11 transformations, 3 ML techniques, and 2 datasets, we find that the improved robustness only applies to the specific transformations used during training data amplification. In other words, the robustified models still rely on unrelated features for predicting the vulnerabilities in the testing data. Additionally, we find that the trained models are unable to generalize to the modified setting which requires to distinguish vulnerable functions from their patches.

Human-In-The-Loop Automatic Program Repair

We introduce Learn2fix, the first human-in-the-loop, semi-automatic repair technique when no bug oracle--except for the user who is reporting the bug--is available. Our approach negotiates with the user the condition under which the bug is observed. Only when a budget of queries to the user is exhausted, it attempts to repair the bug. A query can be thought of as the following question: "When executing this alternative test input, the program produces the following output; is the bug observed"? Through systematic queries, Learn2fix trains an automatic bug oracle that becomes increasingly more accurate in predicting the user's response. Our key challenge is to maximize the oracle's accuracy in predicting which tests are bug-exposing given a small budget of queries. From the alternative tests that were labeled by the user, test-driven automatic repair produces the patch. Our experiments demonstrate that Learn2fix learns a sufficiently accurate automatic oracle with a reasonably low labeling effort (lt. 20 queries). Given Learn2fix's test suite, the GenProg test-driven repair tool produces a higher-quality patch (i.e., passing a larger proportion of validation tests) than using manual test suites provided with the repair benchmark.

MCPA: Program Analysis as Machine Learning

Static program analysis today takes an analytical approach which is quite suitable for a well-scoped system. Data- and control-flow is taken into account. Special cases such as pointers, procedures, and undefined behavior must be handled. A program is analyzed precisely on the statement level. However, the analytical approach is ill-equiped to handle implementations of complex, large-scale, heterogeneous software systems we see in the real world. Existing static analysis techniques that scale, trade correctness (i.e., soundness or completeness) for scalability and build on strong assumptions (e.g., language-specificity). Scalable static analysis are well-known to report errors that do *not* exist (false positives) or fail to report errors that *do* exist (false negatives). Then, how do we know the degree to which the analysis outcome is correct? In this paper, we propose an approach to scale-oblivious greybox program analysis with bounded error which applies efficient approximation schemes (FPRAS) from the foundations of machine learning: PAC learnability. Given two parameters $\delta$ and $\epsilon$, with probability at least $(1-\delta)$, our Monte Carlo Program Analysis (MCPA) approach produces an outcome that has an average error at most $\epsilon$. The parameters $\delta>0$ and $\epsilon>0$ can be chosen arbitrarily close to zero (0) such that the program analysis outcome is said to be probably-approximately correct (PAC). We demonstrate the pertinent concepts of MCPA using three applications: $(\epsilon,\delta)$-approximate quantitative analysis, $(\epsilon,\delta)$-approximate software verification, and $(\epsilon,\delta)$-approximate patch verification.