Daniel Lowd

AAAI Conference 2024 Conference Paper

Provable Robustness against a Union of L_0 Adversarial Attacks

• Zayd Hammoudeh
• Daniel Lowd

Sparse or L0 adversarial attacks arbitrarily perturb an unknown subset of the features. L0 robustness analysis is particularly well-suited for heterogeneous (tabular) data where features have different types or scales. State-of-the-art L0 certified defenses are based on randomized smoothing and apply to evasion attacks only. This paper proposes feature partition aggregation (FPA) -- a certified defense against the union of L0 evasion, backdoor, and poisoning attacks. FPA generates its stronger robustness guarantees via an ensemble whose submodels are trained on disjoint feature sets. Compared to state-of-the-art L0 defenses, FPA is up to 3,000x faster and provides larger median robustness guarantees (e.g., median certificates of 13 pixels over 10 for CIFAR10, 12 pixels over 10 for MNIST, 4 features over 1 for Weather, and 3 features over 1 for Ames), meaning FPA provides the additional dimensions of robustness essentially for free.

JMLR Journal 2023 Journal Article

Adapting and Evaluating Influence-Estimation Methods for Gradient-Boosted Decision Trees

• Jonathan Brophy
• Zayd Hammoudeh
• Daniel Lowd

Influence estimation analyzes how changes to the training data can lead to different model predictions; this analysis can help us better understand these predictions, the models making those predictions, and the data sets they are trained on. However, most influence-estimation techniques are designed for deep learning models with continuous parameters. Gradient-boosted decision trees (GBDTs) are a powerful and widely-used class of models; however, these models are black boxes with opaque decision-making processes. In the pursuit of better understanding GBDT predictions and generally improving these models, we adapt recent and popular influence-estimation methods designed for deep learning models to GBDTs. Specifically, we adapt representer-point methods and TracIn, denoting our new methods TREX and BoostIn, respectively; source code is available at https://github.com/jjbrophy47/treeinfluence. We compare these methods to LeafInfluence and other baselines using 5 different evaluation measures on 22 real-world data sets with 4 popular GBDT implementations. These experiments give us a comprehensive overview of how different approaches to influence estimation work in GBDT models. We find BoostIn is an efficient influence-estimation method for GBDTs that performs equally well or better than existing work while being four orders of magnitude faster. Our evaluation also suggests the gold-standard approach of leave-one-out (LOO) retraining consistently identifies the single-most influential training example but performs poorly at finding the most influential set of training examples for a given target prediction. [abs] [ pdf ][ bib ] [ code ] &copy JMLR 2023. ( edit, beta )

NeurIPS Conference 2022 Conference Paper

Instance-Based Uncertainty Estimation for Gradient-Boosted Regression Trees

• Jonathan Brophy
• Daniel Lowd

Gradient-boosted regression trees (GBRTs) are hugely popular for solving tabular regression problems, but provide no estimate of uncertainty. We propose Instance-Based Uncertainty estimation for Gradient-boosted regression trees (IBUG), a simple method for extending any GBRT point predictor to produce probabilistic predictions. IBUG computes a non-parametric distribution around a prediction using the $k$-nearest training instances, where distance is measured with a tree-ensemble kernel. The runtime of IBUG depends on the number of training examples at each leaf in the ensemble, and can be improved by sampling trees or training instances. Empirically, we find that IBUG achieves similar or better performance than the previous state-of-the-art across 22 benchmark regression datasets. We also find that IBUG can achieve improved probabilistic performance by using different base GBRT models, and can more flexibly model the posterior distribution of a prediction than competing methods. We also find that previous methods suffer from poor probabilistic calibration on some datasets, which can be mitigated using a scalar factor tuned on the validation data. Source code is available at https: //github. com/jjbrophy47/ibug.

ICML Conference 2021 Conference Paper

Machine Unlearning for Random Forests

• Jonathan Brophy
• Daniel Lowd

Responding to user data deletion requests, removing noisy examples, or deleting corrupted training data are just a few reasons for wanting to delete instances from a machine learning (ML) model. However, efficiently removing this data from an ML model is generally difficult. In this paper, we introduce data removal-enabled (DaRE) forests, a variant of random forests that enables the removal of training data with minimal retraining. Model updates for each DaRE tree in the forest are exact, meaning that removing instances from a DaRE model yields exactly the same model as retraining from scratch on updated data. DaRE trees use randomness and caching to make data deletion efficient. The upper levels of DaRE trees use random nodes, which choose split attributes and thresholds uniformly at random. These nodes rarely require updates because they only minimally depend on the data. At the lower levels, splits are chosen to greedily optimize a split criterion such as Gini index or mutual information. DaRE trees cache statistics at each node and training data at each leaf, so that only the necessary subtrees are updated as data is removed. For numerical attributes, greedy nodes optimize over a random subset of thresholds, so that they can maintain statistics while approximating the optimal threshold. By adjusting the number of thresholds considered for greedy nodes, and the number of random nodes, DaRE trees can trade off between more accurate predictions and more efficient updates. In experiments on 13 real-world datasets and one synthetic dataset, we find DaRE forests delete data orders of magnitude faster than retraining from scratch while sacrificing little to no predictive power.

NeurIPS Conference 2020 Conference Paper

Learning from Positive and Unlabeled Data with Arbitrary Positive Shift

• Zayd Hammoudeh
• Daniel Lowd

Positive-unlabeled (PU) learning trains a binary classifier using only positive and unlabeled data. A common simplifying assumption is that the positive data is representative of the target positive class. This assumption rarely holds in practice due to temporal drift, domain shift, and/or adversarial manipulation. This paper shows that PU learning is possible even with arbitrarily non-representative positive data given unlabeled data from the source and target distributions. Our key insight is that only the negative class's distribution need be fixed. We integrate this into two statistically consistent methods to address arbitrary positive bias - one approach combines negative-unlabeled learning with unlabeled-unlabeled learning while the other uses a novel, recursive risk estimator. Experimental results demonstrate our methods' effectiveness across numerous real-world datasets and forms of positive bias, including disjoint positive class-conditional supports. Additionally, we propose a general, simplified approach to address PU risk estimation overfitting.

AAAI Conference 2016 Conference Paper

A Probabilistic Approach to Knowledge Translation

• Shangpu Jiang
• Daniel Lowd
• Dejing Dou

In this paper, we focus on a novel knowledge reuse scenario where the knowledge in the source schema needs to be translated to a semantically heterogeneous target schema. We refer to this task as “knowledge translation” (KT). Unlike data translation and transfer learning, KT does not require any data from the source or target schema. We adopt a probabilistic approach to KT by representing the knowledge in the source schema, the mapping between the source and target schemas, and the resulting knowledge in the target schema all as probability distributions, specially using Markov random fields and Markov logic networks. Given the source knowledge and mappings, we use standard learning and inference algorithms for probabilistic graphical models to find an explicit probability distribution in the target schema that minimizes the Kullback-Leibler divergence from the implicit distribution. This gives us a compact probabilistic model that represents knowledge from the source schema as well as possible, respecting the uncertainty in both the source knowledge and the mapping. In experiments on both propositional and relational domains, we find that the knowledge obtained by KT is comparable to other approaches that require data, demonstrating that knowledge can be reused without data.

AAAI Conference 2016 Conference Paper

Discriminative Structure Learning of Arithmetic Circuits

• Amirmohammad Rooshenas
• Daniel Lowd

The biggest limitation of probabilistic graphical models is the complexity of inference, which is often intractable. An appealing alternative is to use tractable probabilistic models, such as arithmetic circuits (ACs) and sum-product networks (SPNs), in which marginal and conditional queries can be answered efficiently. In this paper, we present the first discriminative structure learning algorithm for ACs, DACLearn (Discriminative AC Learner), which optimizes conditional log-likelihood. Based on our experiments, DACLearn learns models that are more accurate and compact than other tractable generative and discriminative baselines.

JMLR Journal 2015 Journal Article

The Libra Toolkit for Probabilistic Models

• Daniel Lowd
• Amirmohammad Rooshenas

The Libra Toolkit is a collection of algorithms for learning and inference with discrete probabilistic models, including Bayesian networks, Markov networks, dependency networks, and sum-product networks. Compared to other toolkits, Libra places a greater emphasis on learning the structure of tractable models in which exact inference is efficient. It also includes a variety of algorithms for learning graphical models in which inference is potentially intractable, and for performing exact and approximate inference. Libra is released under a 2-clause BSD license to encourage broad use in academia and industry. [abs] [ pdf ][ bib ] [ code ] &copy JMLR 2015. ( edit, beta )

JMLR Journal 2014 Journal Article

Improving Markov Network Structure Learning Using Decision Trees

• Daniel Lowd
• Jesse Davis

Most existing algorithms for learning Markov network structure either are limited to learning interactions among few variables or are very slow, due to the large space of possible structures. In this paper, we propose three new methods for using decision trees to learn Markov network structures. The advantage of using decision trees is that they are very fast to learn and can represent complex interactions among many variables. The first method, DTSL, learns a decision tree to predict each variable and converts each tree into a set of conjunctive features that define the Markov network structure. The second, DT-BLM, builds on DTSL by using it to initialize a search-based Markov network learning algorithm recently proposed by Davis and Domingos (2010). The third, DT+L1, combines the features learned by DTSL with those learned by an L1-regularized logistic regression method (L1) proposed by Ravikumar et al. (2009). In an extensive empirical evaluation on 20 data sets, DTSL is comparable to L1 and significantly faster and more accurate than two other baselines. DT-BLM is slower than DTSL, but obtains slightly higher accuracy. DT+L1 combines the strengths of DTSL and L1 to perform significantly better than either of them with only a modest increase in training time. [abs] [ pdf ][ bib ] &copy JMLR 2014. ( edit, beta )

ICML Conference 2014 Conference Paper

Learning Sum-Product Networks with Direct and Indirect Variable Interactions

• Amirmohammad Rooshenas
• Daniel Lowd

Sum-product networks (SPNs) are a deep probabilistic representation that allows for efficient, exact inference. SPNs generalize many other tractable models, including thin junction trees, latent tree models, and many types of mixtures. Previous work on learning SPN structure has mainly focused on using top-down or bottom-up clustering to find mixtures, which capture variable interactions indirectly through implicit latent variables. In contrast, most work on learning graphical models, thin junction trees, and arithmetic circuits has focused on finding direct interactions among variables. In this paper, we present ID-SPN, a new algorithm for learning SPN structure that unifies the two approaches. In experiments on 20 benchmark datasets, we find that the combination of direct and indirect interactions leads to significantly better accuracy than several state-of-the-art algorithms for learning SPNs and other tractable models.

ICML Conference 2014 Conference Paper

On Robustness and Regularization of Structural Support Vector Machines

• MohamadAli Torkamani
• Daniel Lowd

Previous analysis of binary SVMs has demonstrated a deep connection between robustness to perturbations over uncertainty sets and regularization of the weights. In this paper, we explore the problem of learning robust models for structured prediction problems. We first formulate the problem of learning robust structural SVMs when there are perturbations in the feature space. We consider two different classes of uncertainty sets for the perturbations: ellipsoidal uncertainty sets and polyhedral uncertainty sets. In both cases, we show that the robust optimization problem is equivalent to the non-robust formulation with an additional regularizer. For the ellipsoidal uncertainty set, the additional regularizer is based on the dual norm of the norm that constrains the ellipsoidal uncertainty. For the polyhedral uncertainty set, we show that the robust optimization problem is equivalent to adding a linear regularizer in a transformed weight space related to the linear constraints of the polyhedron. We also show that these constraint sets can be combined and demonstrate a number of interesting special cases. This represents the first theoretical analysis of robust optimization of structural support vector machines. Our experimental results show that our method outperforms the nonrobust structural SVMs on real world data when the test data distributions is drifted from the training data distribution.

ICML Conference 2013 Conference Paper

Convex Adversarial Collective Classification

• MohamadAli Torkamani
• Daniel Lowd

In this paper, we present a novel method for robustly performing collective classification in the presence of a malicious adversary that can modify up to a fixed number of binary-valued attributes. Our method is formulated as a convex quadratic program that guarantees optimal weights against a worst-case adversary in polynomial time. In addition to increased robustness against active adversaries, this kind of adversarial regularization can also lead to improved generalization even when no adversary is present. In experiments on real and simulated data, our method consistently outperforms both non-adversarial and non-relational baselines.

UAI Conference 2012 Conference Paper

Closed-Form Learning of Markov Networks from Dependency Networks

• Daniel Lowd

Markov networks (MNs) are a powerful way to compactly represent a joint probability distribution, but most MN structure learning methods are very slow, due to the high cost of evaluating candidates structures. Dependency networks (DNs) represent a probability distribution as a set of conditional probability distributions. DNs are very fast to learn, but the conditional distributions may be inconsistent with each other and few inference algorithms support DNs. In this paper, we present a closed-form method for converting a DN into an MN, allowing us to enjoy both the efficiency of DN learning and the convenience of the MN representation. When the DN is consistent, this conversion is exact. For inconsistent DNs, we present averaging methods that significantly improve the approximation. In experiments on 12 standard datasets, our methods are orders of magnitude faster than and often more accurate than combining conditional distributions using weight learning.

AAAI Conference 2011 Conference Paper

Mean Field Inference in Dependency Networks: An Empirical Study

• Daniel Lowd
• Arash Shamaei

Dependency networks are a compelling alternative to Bayesian networks for learning joint probability distributions from data and using them to compute probabilities. A dependency network consists of a set of conditional probability distributions, each representing the probability of a single variable given its Markov blanket. Running Gibbs sampling with these conditional distributions produces a joint distribution that can be used to answer queries, but suffers from the traditional slowness of sampling-based inference. In this paper, we observe that the mean field update equation can be applied to dependency networks, even though the conditional probability distributions may be inconsistent with each other. In experiments with learning and inference on 12 datasets, we demonstrate that mean field inference in dependency networks offers similar accuracy to Gibbs sampling but with orders of magnitude improvements in speed. Compared to Bayesian networks learned on the same data, dependency networks offer higher accuracy at greater amounts of evidence. Furthermore, mean field inference is consistently more accurate in dependency networks than in Bayesian networks learned on the same data.

NeurIPS Conference 2010 Conference Paper

Approximate Inference by Compilation to Arithmetic Circuits

• Daniel Lowd
• Pedro Domingos

Arithmetic circuits (ACs) exploit context-specific independence and determinism to allow exact inference even in networks with high treewidth. In this paper, we introduce the first ever approximate inference methods using ACs, for domains where exact inference remains intractable. We propose and evaluate a variety of techniques based on exact compilation, forward sampling, AC structure learning, Markov network parameter learning, variational inference, and Gibbs sampling. In experiments on eight challenging real-world domains, we find that the methods based on sampling and learning work best: one such method (AC2-F) is faster and usually more accurate than loopy belief propagation, mean field, and Gibbs sampling; another (AC2-G) has a running time similar to Gibbs sampling but is consistently more accurate than all baselines.

UAI Conference 2008 Conference Paper

Learning Arithmetic Circuits

• Daniel Lowd
• Pedro M. Domingos

Graphical models are usually learned without regard to the cost of doing inference with them. As a result, even if a good model is learned, it may perform poorly at prediction, because it requires approximate inference. We propose an alternative: learning models with a score function that directly penalizes the cost of inference. Specifically, we learn arithmetic circuits with a penalty on the number of edges in the circuit (in which the cost of inference is linear). Our algorithm is equivalent to learning a Bayesian network with context-specific independence by greedily splitting conditional distributions, at each step scoring the candidates by compiling the resulting network into an arithmetic circuit, and using its size as the penalty. We show how this can be done efficiently, without compiling a circuit from scratch for each candidate. Experiments on several real-world domains show that our algorithm is able to learn tractable models with very large treewidth, and yields more accurate predictions than a standard context-specific Bayesian network learner, in far less time.

IJCAI Conference 2007 Conference Paper

• Daniel Lowd
• Pedro Domingos

A formula in first-order logic can be viewed as a tree, with a logical connective at each node, and a knowledge base can be viewed as a tree whose root is a conjunction. Markov logic [Richardson and Domingos, 2006] makes this conjunction probabilistic, as well as the universal quantifiers directly under it, but the rest of the tree remains purely logical. This causes an asymmetry in the treatment of conjunctions and disjunctions, and of universal and existential quantifiers. We propose to overcome this by allowing the features of Markov logic networks (MLNs) to be nested MLNs. We call this representation recursive random fields (RRFs). RRFs can represent many first-order distributions exponentially more compactly than MLNs. We perform inference in RRFs using MCMC and ICM, and weight learning using a form of backpropagation. Weight learning in RRFs is more powerful than structure learning in MLNs. Applied to first-order knowledge bases, it provides a very flexible form of theory revision. We evaluate RRFs on the problem of probabilistic integrity constraints in databases, and obtain promising results.

ICML Conference 2005 Conference Paper

Naive Bayes models for probability estimation

• Daniel Lowd
• Pedro M. Domingos

Naive Bayes models have been widely used for clustering and classification. However, they are seldom used for general probabilistic learning and inference (i.e., for estimating and computing arbitrary joint, conditional and marginal distributions). In this paper we show that, for a wide range of benchmark datasets, naive Bayes models learned using EM have accuracy and learning time comparable to Bayesian networks with context-specific independence. Most significantly, naive Bayes inference is orders of magnitude faster than Bayesian network inference using Gibbs sampling and belief propagation. This makes naive Bayes models a very attractive alternative to Bayesian networks for general probability estimation, particularly in large or real-time domains.