Margo Seltzer

Zijie J. Wang, Chudi Zhong, Rui Xin et al. · gatech

Given thousands of equally accurate machine learning (ML) models, how can users choose among them? A recent ML technique enables domain experts and data scientists to generate a complete Rashomon set for sparse decision trees--a huge set of almost-optimal interpretable ML models. To help ML practitioners identify models with desirable properties from this Rashomon set, we develop TimberTrek, the first interactive visualization system that summarizes thousands of sparse decision trees at scale. Two usage scenarios highlight how TimberTrek can empower users to easily explore, compare, and curate models that align with their domain knowledge and values. Our open-source tool runs directly in users' computational notebooks and web browsers, lowering the barrier to creating more responsible ML models. TimberTrek is available at the following public demo link: https://poloclub.github.io/timbertrek.

Zakk Heile, Hayden McTavish, Varun Babbar et al.

Standard machine learning pipelines often admit many near-optimal models. These "Rashomon sets" pose a range of challenges and opportunities for uncertainty-aware, robust decision making. They allow users to incorporate domain knowledge and preferences that would otherwise be difficult to specify directly in an objective, and they quantify diversity among valid models for a given training dataset and objective function. However, computation of Rashomon sets, even for simple, interpretable model classes such as sparse decision trees, continues to require immense memory and runtime resources. We present PRAXIS, an algorithm to approximate this Rashomon set with orders of magnitude improvement in runtime and memory usage. We validate that PRAXIS regularly recovers almost all of the full Rashomon set. PRAXIS allows researchers and practitioners to scalably model the Rashomon set for real-world datasets. Code for PRAXIS is available at https://github.com/zakk-h/PRAXIS

Ali Behrouz, Farnoosh Hashemi, Sadaf Sadeghian et al.

Temporal hypergraphs provide a powerful paradigm for modeling time-dependent, higher-order interactions in complex systems. Representation learning for hypergraphs is essential for extracting patterns of the higher-order interactions that are critically important in real-world problems in social network analysis, neuroscience, finance, etc. However, existing methods are typically designed only for specific tasks or static hypergraphs. We present CAT-Walk, an inductive method that learns the underlying dynamic laws that govern the temporal and structural processes underlying a temporal hypergraph. CAT-Walk introduces a temporal, higher-order walk on hypergraphs, SetWalk, that extracts higher-order causal patterns. CAT-Walk uses a novel adaptive and permutation invariant pooling strategy, SetMixer, along with a set-based anonymization process that hides the identity of hyperedges. Finally, we present a simple yet effective neural network model to encode hyperedges. Our evaluation on 10 hypergraph benchmark datasets shows that CAT-Walk attains outstanding performance on temporal hyperedge prediction benchmarks in both inductive and transductive settings. It also shows competitive performance with state-of-the-art methods for node classification. (https://github.com/ubc-systopia/CATWalk)

Rui Xin, Chudi Zhong, Zhi Chen et al.

In any given machine learning problem, there may be many models that could explain the data almost equally well. However, most learning algorithms return only one of these models, leaving practitioners with no practical way to explore alternative models that might have desirable properties beyond what could be expressed within a loss function. The Rashomon set is the set of these all almost-optimal models. Rashomon sets can be extremely complicated, particularly for highly nonlinear function classes that allow complex interaction terms, such as decision trees. We provide the first technique for completely enumerating the Rashomon set for sparse decision trees; in fact, our work provides the first complete enumeration of any Rashomon set for a non-trivial problem with a highly nonlinear discrete function class. This allows the user an unprecedented level of control over model choice among all models that are approximately equally good. We represent the Rashomon set in a specialized data structure that supports efficient querying and sampling. We show three applications of the Rashomon set: 1) it can be used to study variable importance for the set of almost-optimal trees (as opposed to a single tree), 2) the Rashomon set for accuracy enables enumeration of the Rashomon sets for balanced accuracy and F1-score, and 3) the Rashomon set for a full dataset can be used to produce Rashomon sets constructed with only subsets of the data set. Thus, we are able to examine Rashomon sets across problems with a new lens, enabling users to choose models rather than be at the mercy of an algorithm that produces only a single model.

Jiachang Liu, Chudi Zhong, Boxuan Li et al.

Over the last century, risk scores have been the most popular form of predictive model used in healthcare and criminal justice. Risk scores are sparse linear models with integer coefficients; often these models can be memorized or placed on an index card. Typically, risk scores have been created either without data or by rounding logistic regression coefficients, but these methods do not reliably produce high-quality risk scores. Recent work used mathematical programming, which is computationally slow. We introduce an approach for efficiently producing a collection of high-quality risk scores learned from data. Specifically, our approach produces a pool of almost-optimal sparse continuous solutions, each with a different support set, using a beam-search algorithm. Each of these continuous solutions is transformed into a separate risk score through a "star ray" search, where a range of multipliers are considered before rounding the coefficients sequentially to maintain low logistic loss. Our algorithm returns all of these high-quality risk scores for the user to consider. This method completes within minutes and can be valuable in a broad variety of applications.

Chudi Zhong, Zhi Chen, Jiachang Liu et al.

In real applications, interaction between machine learning models and domain experts is critical; however, the classical machine learning paradigm that usually produces only a single model does not facilitate such interaction. Approximating and exploring the Rashomon set, i.e., the set of all near-optimal models, addresses this practical challenge by providing the user with a searchable space containing a diverse set of models from which domain experts can choose. We present algorithms to efficiently and accurately approximate the Rashomon set of sparse, generalized additive models with ellipsoids for fixed support sets and use these ellipsoids to approximate Rashomon sets for many different support sets. The approximated Rashomon set serves as a cornerstone to solve practical challenges such as (1) studying the variable importance for the model class; (2) finding models under user-specified constraints (monotonicity, direct editing); and (3) investigating sudden changes in the shape functions. Experiments demonstrate the fidelity of the approximated Rashomon set and its effectiveness in solving practical challenges.

Ali Behrouz, Margo Seltzer

The problem of identifying anomalies in dynamic networks is a fundamental task with a wide range of applications. However, it raises critical challenges due to the complex nature of anomalies, lack of ground truth knowledge, and complex and dynamic interactions in the network. Most existing approaches usually study networks with a single type of connection between vertices, while in many applications interactions between objects vary, yielding multiplex networks. We propose ANOMULY, a general, unsupervised edge anomaly detection framework for multiplex dynamic networks. In each relation type, ANOMULY sees node embeddings at different GNN layers as hierarchical node states and employs a GRU cell to capture temporal properties of the network and update node embeddings over time. We then add an attention mechanism that incorporates information across different types of relations. Our case study on brain networks shows how this approach could be employed as a new tool to understand abnormal brain activity that might reveal a brain disease or disorder. Extensive experiments on nine real-world datasets demonstrate that ANOMULY achieves state-of-the-art performance.

Rui Zhang, Rui Xin, Margo Seltzer et al.

Regression trees are one of the oldest forms of AI models, and their predictions can be made without a calculator, which makes them broadly useful, particularly for high-stakes applications. Within the large literature on regression trees, there has been little effort towards full provable optimization, mainly due to the computational hardness of the problem. This work proposes a dynamic-programming-with-bounds approach to the construction of provably-optimal sparse regression trees. We leverage a novel lower bound based on an optimal solution to the k-Means clustering algorithm in 1-dimension over the set of labels. We are often able to find optimal sparse trees in seconds, even for challenging datasets that involve large numbers of samples and highly-correlated features.

Ali Behrouz, Mathias Lecuyer, Cynthia Rudin et al.

Sparse decision trees are one of the most common forms of interpretable models. While recent advances have produced algorithms that fully optimize sparse decision trees for prediction, that work does not address policy design, because the algorithms cannot handle weighted data samples. Specifically, they rely on the discreteness of the loss function, which means that real-valued weights cannot be directly used. For example, none of the existing techniques produce policies that incorporate inverse propensity weighting on individual data points. We present three algorithms for efficient sparse weighted decision tree optimization. The first approach directly optimizes the weighted loss function; however, it tends to be computationally inefficient for large datasets. Our second approach, which scales more efficiently, transforms weights to integer values and uses data duplication to transform the weighted decision tree optimization problem into an unweighted (but larger) counterpart. Our third algorithm, which scales to much larger datasets, uses a randomized procedure that samples each data point with a probability proportional to its weight. We present theoretical bounds on the error of the two fast methods and show experimentally that these methods can be two orders of magnitude faster than the direct optimization of the weighted loss, without losing significant accuracy.

Cynthia Rudin, Chudi Zhong, Lesia Semenova et al.

The Rashomon Effect, coined by Leo Breiman, describes the phenomenon that there exist many equally good predictive models for the same dataset. This phenomenon happens for many real datasets and when it does, it sparks both magic and consternation, but mostly magic. In light of the Rashomon Effect, this perspective piece proposes reshaping the way we think about machine learning, particularly for tabular data problems in the nondeterministic (noisy) setting. We address how the Rashomon Effect impacts (1) the existence of simple-yet-accurate models, (2) flexibility to address user preferences, such as fairness and monotonicity, without losing performance, (3) uncertainty in predictions, fairness, and explanations, (4) reliable variable importance, (5) algorithm choice, specifically, providing advanced knowledge of which algorithms might be suitable for a given problem, and (6) public policy. We also discuss a theory of when the Rashomon Effect occurs and why. Our goal is to illustrate how the Rashomon Effect can have a massive impact on the use of machine learning for complex problems in society.

Xiyang Hu, Cynthia Rudin, Margo Seltzer

Decision tree algorithms have been among the most popular algorithms for interpretable (transparent) machine learning since the early 1980's. The problem that has plagued decision tree algorithms since their inception is their lack of optimality, or lack of guarantees of closeness to optimality: decision tree algorithms are often greedy or myopic, and sometimes produce unquestionably suboptimal models. Hardness of decision tree optimization is both a theoretical and practical obstacle, and even careful mathematical programming approaches have not been able to solve these problems efficiently. This work introduces the first practical algorithm for optimal decision trees for binary variables. The algorithm is a co-design of analytical bounds that reduce the search space and modern systems techniques, including data structures and a custom bit-vector library. Our experiments highlight advantages in scalability, speed, and proof of optimality. The code is available at https://github.com/xiyanghu/OSDT.

Hayden McTavish, Jon Donnelly, Margo Seltzer et al.

Many important datasets contain samples that are missing one or more feature values. Maintaining the interpretability of machine learning models in the presence of such missing data is challenging. Singly or multiply imputing missing values complicates the model's mapping from features to labels. On the other hand, reasoning on indicator variables that represent missingness introduces a potentially large number of additional terms, sacrificing sparsity. We solve these problems with M-GAM, a sparse, generalized, additive modeling approach that incorporates missingness indicators and their interaction terms while maintaining sparsity through l0 regularization. We show that M-GAM provides similar or superior accuracy to prior methods while significantly improving sparsity relative to either imputation or naive inclusion of indicator variables.

Rui Zhang, Rui Xin, Margo Seltzer et al.

Interpretability is crucial for doctors, hospitals, pharmaceutical companies and biotechnology corporations to analyze and make decisions for high stakes problems that involve human health. Tree-based methods have been widely adopted for survival analysis due to their appealing interpretablility and their ability to capture complex relationships. However, most existing methods to produce survival trees rely on heuristic (or greedy) algorithms, which risk producing sub-optimal models. We present a dynamic-programming-with-bounds approach that finds provably-optimal sparse survival tree models, frequently in only a few seconds.

Varun Babbar, Hayden McTavish, Cynthia Rudin et al.

Decision tree optimization is fundamental to interpretable machine learning. The most popular approach is to greedily search for the best feature at every decision point, which is fast but provably suboptimal. Recent approaches find the global optimum using branch and bound with dynamic programming, showing substantial improvements in accuracy and sparsity at great cost to scalability. An ideal solution would have the accuracy of an optimal method and the scalability of a greedy method. We introduce a family of algorithms called SPLIT (SParse Lookahead for Interpretable Trees) that moves us significantly forward in achieving this ideal balance. We demonstrate that not all sub-problems need to be solved to optimality to find high quality trees; greediness suffices near the leaves. Since each depth adds an exponential number of possible trees, this change makes our algorithms orders of magnitude faster than existing optimal methods, with negligible loss in performance. We extend this algorithm to allow scalable computation of sets of near-optimal trees (i.e., the Rashomon set).

Hayden McTavish, Zachery Boner, Jon Donnelly et al.

Decision trees are widely used for interpretable machine learning due to their clearly structured reasoning process. However, this structure belies a challenge we refer to as predictive equivalence: a given tree's decision boundary can be represented by many different decision trees. The presence of models with identical decision boundaries but different evaluation processes makes model selection challenging. The models will have different variable importance and behave differently in the presence of missing values, but most optimization procedures will arbitrarily choose one such model to return. We present a boolean logical representation of decision trees that does not exhibit predictive equivalence and is faithful to the underlying decision boundary. We apply our representation to several downstream machine learning tasks. Using our representation, we show that decision trees are surprisingly robust to test-time missingness of feature values; we address predictive equivalence's impact on quantifying variable importance; and we present an algorithm to optimize the cost of reaching predictions.

Jiachang Liu, Chudi Zhong, Margo Seltzer et al.

We present fast classification techniques for sparse generalized linear and additive models. These techniques can handle thousands of features and thousands of observations in minutes, even in the presence of many highly correlated features. For fast sparse logistic regression, our computational speed-up over other best-subset search techniques owes to linear and quadratic surrogate cuts for the logistic loss that allow us to efficiently screen features for elimination, as well as use of a priority queue that favors a more uniform exploration of features. As an alternative to the logistic loss, we propose the exponential loss, which permits an analytical solution to the line search at each iteration. Our algorithms are generally 2 to 5 times faster than previous approaches. They produce interpretable models that have accuracy comparable to black box models on challenging datasets.

Hayden McTavish, Chudi Zhong, Reto Achermann et al.

Sparse decision tree optimization has been one of the most fundamental problems in AI since its inception and is a challenge at the core of interpretable machine learning. Sparse decision tree optimization is computationally hard, and despite steady effort since the 1960's, breakthroughs have only been made on the problem within the past few years, primarily on the problem of finding optimal sparse decision trees. However, current state-of-the-art algorithms often require impractical amounts of computation time and memory to find optimal or near-optimal trees for some real-world datasets, particularly those having several continuous-valued features. Given that the search spaces of these decision tree optimization problems are massive, can we practically hope to find a sparse decision tree that competes in accuracy with a black box machine learning model? We address this problem via smart guessing strategies that can be applied to any optimal branch-and-bound-based decision tree algorithm. We show that by using these guesses, we can reduce the run time by multiple orders of magnitude, while providing bounds on how far the resulting trees can deviate from the black box's accuracy and expressive power. Our approach enables guesses about how to bin continuous features, the size of the tree, and lower bounds on the error for the optimal decision tree. Our experiments show that in many cases we can rapidly construct sparse decision trees that match the accuracy of black box models. To summarize: when you are having trouble optimizing, just guess.

Xueyuan Han, Xiao Yu, Thomas Pasquier et al.

Many users implicitly assume that software can only be exploited after it is installed. However, recent supply-chain attacks demonstrate that application integrity must be ensured during installation itself. We introduce SIGL, a new tool for detecting malicious behavior during software installation. SIGL collects traces of system call activity, building a data provenance graph that it analyzes using a novel autoencoder architecture with a graph long short-term memory network (graph LSTM) for the encoder and a standard multilayer perceptron for the decoder. SIGL flags suspicious installations as well as the specific installation-time processes that are likely to be malicious. Using a test corpus of 625 malicious installers containing real-world malware, we demonstrate that SIGL has a detection accuracy of 96%, outperforming similar systems from industry and academia by up to 87% in precision and recall and 45% in accuracy. We also demonstrate that SIGL can pinpoint the processes most likely to have triggered malicious behavior, works on different audit platforms and operating systems, and is robust to training data contamination and adversarial attack. It can be used with application-specific models, even in the presence of new software versions, as well as application-agnostic meta-models that encompass a wide range of applications and installers.

Jimmy Lin, Chudi Zhong, Diane Hu et al.

Decision tree optimization is notoriously difficult from a computational perspective but essential for the field of interpretable machine learning. Despite efforts over the past 40 years, only recently have optimization breakthroughs been made that have allowed practical algorithms to find optimal decision trees. These new techniques have the potential to trigger a paradigm shift where it is possible to construct sparse decision trees to efficiently optimize a variety of objective functions without relying on greedy splitting and pruning heuristics that often lead to suboptimal solutions. The contribution in this work is to provide a general framework for decision tree optimization that addresses the two significant open problems in the area: treatment of imbalanced data and fully optimizing over continuous variables. We present techniques that produce optimal decision trees over a variety of objectives including F-score, AUC, and partial area under the ROC convex hull. We also introduce a scalable algorithm that produces provably optimal results in the presence of continuous variables and speeds up decision tree construction by several orders of magnitude relative to the state-of-the art.

Xueyuan Han, James Mickens, Ashish Gehani et al.

Host-based anomaly detectors generate alarms by inspecting audit logs for suspicious behavior. Unfortunately, evaluating these anomaly detectors is hard. There are few high-quality, publicly-available audit logs, and there are no pre-existing frameworks that enable push-button creation of realistic system traces. To make trace generation easier, we created Xanthus, an automated tool that orchestrates virtual machines to generate realistic audit logs. Using Xanthus' simple management interface, administrators select a base VM image, configure a particular tracing framework to use within that VM, and define post-launch scripts that collect and save trace data. Once data collection is finished, Xanthus creates a self-describing archive, which contains the VM, its configuration parameters, and the collected trace data. We demonstrate that Xanthus hides many of the tedious (yet subtle) orchestration tasks that humans often get wrong; Xanthus avoids mistakes that lead to non-replicable experiments.

Xueyuan Han, Thomas Pasquier, Adam Bates et al.

Advanced Persistent Threats (APTs) are difficult to detect due to their "low-and-slow" attack patterns and frequent use of zero-day exploits. We present UNICORN, an anomaly-based APT detector that effectively leverages data provenance analysis. From modeling to detection, UNICORN tailors its design specifically for the unique characteristics of APTs. Through extensive yet time-efficient graph analysis, UNICORN explores provenance graphs that provide rich contextual and historical information to identify stealthy anomalous activities without pre-defined attack signatures. Using a graph sketching technique, it summarizes long-running system execution with space efficiency to combat slow-acting attacks that take place over a long time span. UNICORN further improves its detection capability using a novel modeling approach to understand long-term behavior as the system evolves. Our evaluation shows that UNICORN outperforms an existing state-of-the-art APT detection system and detects real-life APT scenarios with high accuracy.

Sheung Chi Chan, James Cheney, Pramod Bhatotia et al.

System level provenance is of widespread interest for applications such as security enforcement and information protection. However, testing the correctness or completeness of provenance capture tools is challenging and currently done manually. In some cases there is not even a clear consensus about what behavior is correct. We present an automated tool, ProvMark, that uses an existing provenance system as a black box and reliably identifies the provenance graph structure recorded for a given activity, by a reduction to subgraph isomorphism problems handled by an external solver. ProvMark is a beginning step in the much needed area of testing and comparing the expressiveness of provenance systems. We demonstrate ProvMark's usefuless in comparing three capture systems with different architectures and distinct design philosophies.

Thomas Pasquier, Xueyuan Han, Thomas Moyer et al.

Identifying the root cause and impact of a system intrusion remains a foundational challenge in computer security. Digital provenance provides a detailed history of the flow of information within a computing system, connecting suspicious events to their root causes. Although existing provenance-based auditing techniques provide value in forensic analysis, they assume that such analysis takes place only retrospectively. Such post-hoc analysis is insufficient for realtime security applications, moreover, even for forensic tasks, prior provenance collection systems exhibited poor performance and scalability, jeopardizing the timeliness of query responses. We present CamQuery, which provides inline, realtime provenance analysis, making it suitable for implementing security applications. CamQuery is a Linux Security Module that offers support for both userspace and in-kernel execution of analysis applications. We demonstrate the applicability of CamQuery to a variety of runtime security applications including data loss prevention, intrusion detection, and regulatory compliance. In evaluation, we demonstrate that CamQuery reduces the latency of realtime query mechanisms, while imposing minimal overheads on system execution. CamQuery thus enables the further deployment of provenance-based technologies to address central challenges in computer security.

Xueyuan Han, Thomas Pasquier, Margo Seltzer

Intrusion detection is an arms race; attackers evade intrusion detection systems by developing new attack vectors to sidestep known defense mechanisms. Provenance provides a detailed, structured history of the interactions of digital objects within a system. It is ideal for intrusion detection, because it offers a holistic, attack-vector-agnostic view of system execution. As such, provenance graph analysis fundamentally strengthens detection robustness. We discuss the opportunities and challenges associated with provenance-based intrusion detection and provide insights based on our experience building such systems.

Xueyuan Han, Thomas Pasquier, Tanvi Ranjan et al.

We present FRAPpuccino (or FRAP), a provenance-based fault detection mechanism for Platform as a Service (PaaS) users, who run many instances of an application on a large cluster of machines. FRAP models, records, and analyzes the behavior of an application and its impact on the system as a directed acyclic provenance graph. It assumes that most instances behave normally and uses their behavior to construct a model of legitimate behavior. Given a model of legitimate behavior, FRAP uses a dynamic sliding window algorithm to compare a new instance's execution to that of the model. Any instance that does not conform to the model is identified as an anomaly. We present the FRAP prototype and experimental results showing that it can accurately detect application anomalies.

Thomas Pasquier, Xueyuan Han, Mark Goldstein et al.

Data provenance describes how data came to be in its present form. It includes data sources and the transformations that have been applied to them. Data provenance has many uses, from forensics and security to aiding the reproducibility of scientific experiments. We present CamFlow, a whole-system provenance capture mechanism that integrates easily into a PaaS offering. While there have been several prior whole-system provenance systems that captured a comprehensive, systemic and ubiquitous record of a system's behavior, none have been widely adopted. They either A) impose too much overhead, B) are designed for long-outdated kernel releases and are hard to port to current systems, C) generate too much data, or D) are designed for a single system. CamFlow addresses these shortcoming by: 1) leveraging the latest kernel design advances to achieve efficiency; 2) using a self-contained, easily maintainable implementation relying on a Linux Security Module, NetFilter, and other existing kernel facilities; 3) providing a mechanism to tailor the captured provenance data to the needs of the application; and 4) making it easy to integrate provenance across distributed systems. The provenance we capture is streamed and consumed by tenant-built auditor applications. We illustrate the usability of our implementation by describing three such applications: demonstrating compliance with data regulations; performing fault/intrusion detection; and implementing data loss prevention. We also show how CamFlow can be leveraged to capture meaningful provenance without modifying existing applications.

Elaine Angelino, Nicholas Larus-Stone, Daniel Alabi et al.

We present the design and implementation of a custom discrete optimization technique for building rule lists over a categorical feature space. Our algorithm produces rule lists with optimal training performance, according to the regularized empirical risk, with a certificate of optimality. By leveraging algorithmic bounds, efficient data structures, and computational reuse, we achieve several orders of magnitude speedup in time and a massive reduction of memory consumption. We demonstrate that our approach produces optimal rule lists on practical problems in seconds. Our results indicate that it is possible to construct optimal sparse rule lists that are approximately as accurate as the COMPAS proprietary risk prediction tool on data from Broward County, Florida, but that are completely interpretable. This framework is a novel alternative to CART and other decision tree methods for interpretable modeling.

Jacob Whitehill, Margo Seltzer

We investigated the feasibility of crowdsourcing full-fledged tutorial videos from ordinary people on the Web on how to solve math problems related to logarithms. This kind of approach (a form of learnersourcing) to efficiently collecting tutorial videos and other learning resources could be useful for realizing personalized learning-at-scale, whereby students receive specific learning resources -- drawn from a large and diverse set -- that are tailored to their individual and time-varying needs. Results of our study, in which we collected 399 videos from 66 unique "teachers" on Mechanical Turk, suggest that (1) approximately 100 videos -- over $80\%$ of which are mathematically fully correct -- can be crowdsourced per week for \$5/video; (2) the crowdsourced videos exhibit significant diversity in terms of language style, presentation media, and pedagogical approach; (3) the average learning gains (posttest minus pretest score) associated with watching the videos was stat.~sig.~higher than for a control video ($0.105$ versus $0.045$); and (4) the average learning gains ($0.1416$) from watching the best tested crowdsourced videos was comparable to the learning gains ($0.1506$) from watching a popular Khan Academy video on logarithms.

Hongyu Yang, Cynthia Rudin, Margo Seltzer

We present an algorithm for building probabilistic rule lists that is two orders of magnitude faster than previous work. Rule list algorithms are competitors for decision tree algorithms. They are associative classifiers, in that they are built from pre-mined association rules. They have a logical structure that is a sequence of IF-THEN rules, identical to a decision list or one-sided decision tree. Instead of using greedy splitting and pruning like decision tree algorithms, we fully optimize over rule lists, striking a practical balance between accuracy, interpretability, and computational speed. The algorithm presented here uses a mixture of theoretical bounds (tight enough to have practical implications as a screening or bounding procedure), computational reuse, and highly tuned language libraries to achieve computational efficiency. Currently, for many practical problems, this method achieves better accuracy and sparsity than decision trees; further, in many cases, the computational time is practical and often less than that of decision trees. The result is a probabilistic classifier (which estimates P(y = 1|x) for each x) that optimizes the posterior of a Bayesian hierarchical model over rule lists.

Elaine Angelino, Eddie Kohler, Amos Waterland et al.

We present a general framework for accelerating a large class of widely used Markov chain Monte Carlo (MCMC) algorithms. Our approach exploits fast, iterative approximations to the target density to speculatively evaluate many potential future steps of the chain in parallel. The approach can accelerate computation of the target distribution of a Bayesian inference problem, without compromising exactness, by exploiting subsets of data. It takes advantage of whatever parallel resources are available, but produces results exactly equivalent to standard serial execution. In the initial burn-in phase of chain evaluation, it achieves speedup over serial evaluation that is close to linear in the number of available cores.