The goal of Root Cause Analysis (RCA) is to explain why an anomaly occurred by identifying where the fault originated. Several recent works model the anomalous event as resulting from a change in the causal mechanism at the root cause, i.e., as a soft intervention. RCA is then the task of identifying which causal mechanism changed. In real-world applications, one often has either few or only a single sample from the post-intervention distribution: a severe limitation for most methods, which assume one knows or can estimate the distribution. However, even those that do not are statistically ill-posed due to the need to probe regression models in regions of low probability density. In this paper, we propose simple, efficient methods to overcome both difficulties in the case where there is a single root cause and the causal graph is a polytree. When one knows the causal graph, we give guarantees for a traversal algorithm that requires only marginal anomaly scores and does not depend on specifying an arbitrary anomaly score cut-off. When one does not know the causal graph, we show that the heuristic of identifying root causes as the variables with the highest marginal anomaly scores is causally justified. To this end, we prove that anomalies with small scores are unlikely to cause those with larger scores in polytrees and give upper bounds for the likelihood of causal pathways with non-monotonic anomaly scores.

Decision support systems based on prediction sets have proven to be effective at helping human experts solve classification tasks. Rather than providing single-label predictions, these systems provide sets of label predictions constructed using conformal prediction, namely prediction sets, and ask human experts to predict label values from these sets. In this paper, we first show that the prediction sets constructed using conformal prediction are, in general, suboptimal in terms of average accuracy. Then, we show that the problem of finding the optimal prediction sets under which the human experts achieve the highest average accuracy is NP-hard. More strongly, unless P = NP, we show that the problem is hard to approximate to any factor less than the size of the label set. However, we introduce a simple and efficient greedy algorithm that, for a large class of expert models and non-conformity scores, is guaranteed to find prediction sets that provably offer equal or greater performance than those constructed using conformal prediction. Further, using a simulation study with both synthetic and real expert predictions, we demonstrate that, in practice, our greedy algorithm finds near-optimal prediction sets offering greater performance than conformal prediction.

Screening classifiers are increasingly used to identify qualified candidates in a variety of selection processes. In this context, it has been recently shown that if a classifier is calibrated, one can identify the smallest set of candidates which contains, in expectation, a desired number of qualified candidates using a threshold decision rule. This lends support to focusing on calibration as the only requirement for screening classifiers. In this paper, we argue that screening policies that use calibrated classifiers may suffer from an understudied type of within-group unfairness—they may unfairly treat qualified members within demographic groups of interest. Further, we argue that this type of unfairness can be avoided if classifiers satisfy within-group monotonicity, a natural monotonicity property within each group. Then, we introduce an efficient post-processing algorithm based on dynamic programming to minimally modify a given calibrated classifier so that its probability estimates satisfy within-group monotonicity. We validate our algorithm using US Census survey data and show that within-group monotonicity can often be achieved at a small cost in terms of prediction granularity and shortlist size.

Automated decision support systems promise to help human experts solve multiclass classification tasks more efficiently and accurately. However, existing systems typically require experts to understand when to cede agency to the system or when to exercise their own agency. Otherwise, the experts may be better off solving the classification tasks on their own. In this work, we develop an automated decision support system that, by design, does not require experts to understand when to trust the system to improve performance. Rather than providing (single) label predictions and letting experts decide when to trust these predictions, our system provides sets of label predictions constructed using conformal prediction—prediction sets—and forcefully asks experts to predict labels from these sets. By using conformal prediction, our system can precisely trade-off the probability that the true label is not in the prediction set, which determines how frequently our system will mislead the experts, and the size of the prediction set, which determines the difficulty of the classification task the experts need to solve using our system. In addition, we develop an efficient and near-optimal search method to find the conformal predictor under which the experts benefit the most from using our system. Simulation experiments using synthetic and real expert predictions demonstrate that our system may help experts make more accurate predictions and is robust to the accuracy of the classifier the conformal predictor relies on.

Most supervised learning models are trained for full automation. However, their predictions are sometimes worse than those by human experts on some specific instances. Motivated by this empirical observation, our goal is to design classifiers that are optimized to operate under different automation levels. More specifically, we focus on convex margin-based classifiers and first show that the problem is NP-hard. Then, we further show that, for support vector machines, the corresponding objective function can be expressed as the difference of two functions f = g - c, where g is monotone, non-negative and gamma-weakly submodular, and c is non-negative and modular. This representation allows a recently introduced deterministic greedy algorithm, as well as a more efficient randomized variant of the algorithm, to enjoy approximation guarantees at solving the problem. Experiments on synthetic and real-world data from several applications in medical diagnosis illustrate our theoretical findings and demonstrate that, under human assistance, supervised learning models trained to operate under different automation levels can outperform those trained for full automation as well as humans operating alone.

Multiple lines of evidence suggest that predictive models may benefit from algorithmic triage. Under algorithmic triage, a predictive model does not predict all instances but instead defers some of them to human experts. However, the interplay between the prediction accuracy of the model and the human experts under algorithmic triage is not well understood. In this work, we start by formally characterizing under which circumstances a predictive model may benefit from algorithmic triage. In doing so, we also demonstrate that models trained for full automation may be suboptimal under triage. Then, given any model and desired level of triage, we show that the optimal triage policy is a deterministic threshold rule in which triage decisions are derived deterministically by thresholding the difference between the model and human errors on a per-instance level. Building upon these results, we introduce a practical gradient-based algorithm that is guaranteed to find a sequence of predictive models and triage policies of increasing performance. Experiments on a wide variety of supervised learning tasks using synthetic and real data from two important applications---content moderation and scientific discovery---illustrate our theoretical results and show that the models and triage policies provided by our gradient-based algorithm outperform those provided by several competitive baselines.

There is a huge gap between the speeds of modern caches and main memories, and therefore cache misses account for a considerable loss of efficiency in programs. The predominant technique to address this issue has been Data Packing: data elements that are frequently accessed within time proximity are packed into the same cache block, thereby minimizing accesses to the main memory. We consider the algorithmic problem of Data Packing on a two-level memory system. Given a reference sequence R of accesses to data elements, the task is to partition the elements into cache blocks such that the number of cache misses on R is minimized. The problem is notoriously difficult: it is NP-hard even when the cache has size 1, and is hard to approximate for any cache size larger than 4. Therefore, all existing techniques for Data Packing are based on heuristics and lack theoretical guarantees. In this work, we present the first positive theoretical results for Data Packing, along with new and stronger negative results. We consider the problem under the lens of the underlying access hypergraphs, which are hypergraphs of affinities between the data elements, where the order of an access hypergraph corresponds to the size of the affinity group. We study the problem parameterized by the treewidth of access hypergraphs, which is a standard notion in graph theory to measure the closeness of a graph to a tree. Our main results are as follows: we show that there is a number q * depending on the cache parameters such that (a) if the access hypergraph of order q * has constant treewidth, then there is a linear-time algorithm for Data Packing; (b) the Data Packing problem remains NP-hard even if the access hypergraph of order q * −1 has constant treewidth. Thus, we establish a fine-grained dichotomy depending on a single parameter, namely, the highest order among access hypegraphs that have constant treewidth; and establish the optimal value q * of this parameter. Finally, we present an experimental evaluation of a prototype implementation of our algorithm. Our results demonstrate that, in practice, access hypergraphs of many commonly-used algorithms have small treewidth. We compare our approach with several state-of-the-art heuristic-based algorithms and show that our algorithm leads to significantly fewer cache-misses.

We consider the stochastic shortest path (SSP) problem for succinct Markov decision processes (MDPs), where the MDP consists of a set of variables, and a set of nondeterministic rules that update the variables. First, we show that several examples from the AI literature can be modeled as succinct MDPs. Then we present computational approaches for upper and lower bounds for the SSP problem: (a) for computing upper bounds, our method is polynomial-time in the implicit description of the MDP; (b) for lower bounds, we present a polynomial-time (in the size of the implicit description) reduction to quadratic programming. Our approach is applicable even to infinite-state MDPs. Finally, we present experimental results to demonstrate the effectiveness of our approach on several classical examples from the AI literature.