An Axiomatic Approach to Model-Agnostic Concept Explanations

Concept explanation is a popular approach for examining how human-interpretable concepts impact the predictions of a model. However, most existing methods for concept explanations are tailored to specific models. To address this issue, this paper focuses on model-agnostic measures. Specifically, we propose an approach to concept explanations that satisfy three natural axioms: linearity, recursivity, and similarity. We then establish connections with previous concept explanation methods, offering insight into their varying semantic meanings. Experimentally, we demonstrate the utility of the new method by applying it in different scenarios: for model selection, optimizer selection, and model improvement using a kind of prompt editing for zero-shot vision language models.

Principal-Agent Reward Shaping in MDPs

Principal-agent problems arise when one party acts on behalf of another, leading to conflicts of interest. The economic literature has extensively studied principal-agent problems, and recent work has extended this to more complex scenarios such as Markov Decision Processes (MDPs). In this paper, we further explore this line of research by investigating how reward shaping under budget constraints can improve the principal's utility. We study a two-player Stackelberg game where the principal and the agent have different reward functions, and the agent chooses an MDP policy for both players. The principal offers an additional reward to the agent, and the agent picks their policy selfishly to maximize their reward, which is the sum of the original and the offered reward. Our results establish the NP-hardness of the problem and offer polynomial approximation algorithms for two classes of instances: Stochastic trees and deterministic decision processes with a finite horizon.

A Learning-Theoretic Framework for Certified Auditing of Machine Learning Models

Responsible use of machine learning requires that models be audited for undesirable properties. However, how to do principled auditing in a general setting has remained ill-understood. In this paper, we propose a formal learning-theoretic framework for auditing. We propose algorithms for auditing linear classifiers for feature sensitivity using label queries as well as different kinds of explanations, and provide performance guarantees. Our results illustrate that while counterfactual explanations can be extremely helpful for auditing, anchor explanations may not be as beneficial in the worst case.

There is no Accuracy-Interpretability Tradeoff in Reinforcement Learning for Mazes

Interpretability is an essential building block for trustworthiness in reinforcement learning systems. However, interpretability might come at the cost of deteriorated performance, leading many researchers to build complex models. Our goal is to analyze the cost of interpretability. We show that in certain cases, one can achieve policy interpretability while maintaining its optimality. We focus on a classical problem from reinforcement learning: mazes with $k$ obstacles in $\mathbb{R}^d$. We prove the existence of a small decision tree with a linear function at each inner node and depth $O(\log k + 2^d)$ that represents an optimal policy. Note that for the interesting case of a constant $d$, we have $O(\log k)$ depth. Thus, in this setting, there is no accuracy-interpretability tradeoff. To prove this result, we use a new "compressing" technique that might be useful in additional settings.

Finding Safe Zones of policies Markov Decision Processes

Given a policy, we define a SafeZone as a subset of states, such that most of the policy's trajectories are confined to this subset. The quality of the SafeZone is parameterized by the number of states and the escape probability, i.e., the probability that a random trajectory will leave the subset. SafeZones are especially interesting when they have a small number of states and low escape probability. We study the complexity of finding optimal SafeZones, and show that in general the problem is computationally hard. For this reason we concentrate on computing approximate SafeZones. Our main result is a bi-criteria approximation algorithm which gives a factor of almost $2$ approximation for both the escape probability and SafeZone size, using a polynomial size sample complexity. We conclude the paper with an empirical evaluation of our algorithm.

Framework for Evaluating Faithfulness of Local Explanations

We study the faithfulness of an explanation system to the underlying prediction model. We show that this can be captured by two properties, consistency and sufficiency, and introduce quantitative measures of the extent to which these hold. Interestingly, these measures depend on the test-time data distribution. For a variety of existing explanation systems, such as anchors, we analytically study these quantities. We also provide estimators and sample complexity bounds for empirically determining the faithfulness of black-box explanation systems. Finally, we experimentally validate the new properties and estimators.

Connecting Interpretability and Robustness in Decision Trees through Separation

Recent research has recognized interpretability and robustness as essential properties of trustworthy classification. Curiously, a connection between robustness and interpretability was empirically observed, but the theoretical reasoning behind it remained elusive. In this paper, we rigorously investigate this connection. Specifically, we focus on interpretation using decision trees and robustness to $l_{\infty}$-perturbation. Previous works defined the notion of $r$-separation as a sufficient condition for robustness. We prove upper and lower bounds on the tree size in case the data is $r$-separated. We then show that a tighter bound on the size is possible when the data is linearly separated. We provide the first algorithm with provable guarantees both on robustness, interpretability, and accuracy in the context of decision trees. Experiments confirm that our algorithm yields classifiers that are both interpretable and robust and have high accuracy. The code for the experiments is available at https://github.com/yangarbiter/interpretable-robust-trees .

Bounded Memory Active Learning through Enriched Queries

The explosive growth of easily-accessible unlabeled data has lead to growing interest in active learning, a paradigm in which data-hungry learning algorithms adaptively select informative examples in order to lower prohibitively expensive labeling costs. Unfortunately, in standard worst-case models of learning, the active setting often provides no improvement over non-adaptive algorithms. To combat this, a series of recent works have considered a model in which the learner may ask enriched queries beyond labels. While such models have seen success in drastically lowering label costs, they tend to come at the expense of requiring large amounts of memory. In this work, we study what families of classifiers can be learned in bounded memory. To this end, we introduce a novel streaming-variant of enriched-query active learning along with a natural combinatorial parameter called lossless sample compression that is sufficient for learning not only with bounded memory, but in a query-optimal and computationally efficient manner as well. Finally, we give three fundamental examples of classifier families with small, easy to compute lossless compression schemes when given access to basic enriched queries: axis-aligned rectangles, decision trees, and halfspaces in two dimensions.

A Constant Approximation Algorithm for Sequential No-Substitution k-Median Clustering under a Random Arrival Order

We study k-median clustering under the sequential no-substitution setting. In this setting, a data stream is sequentially observed, and some of the points are selected by the algorithm as cluster centers. However, a point can be selected as a center only immediately after it is observed, before observing the next point. In addition, a selected center cannot be substituted later. We give a new algorithm for this setting that obtains a constant approximation factor on the optimal risk under a random arrival order. This is the first such algorithm that holds without any assumptions on the input data and selects a non-trivial number of centers. The number of selected centers is quasi-linear in k. Our algorithm and analysis are based on a careful risk estimation that avoids outliers, a new concept of a linear bin division, and repeated calculations using an offline clustering algorithm.

No-substitution k-means Clustering with Adversarial Order

We investigate $k$-means clustering in the online no-substitution setting when the input arrives in \emph{arbitrary} order. In this setting, points arrive one after another, and the algorithm is required to instantly decide whether to take the current point as a center before observing the next point. Decisions are irrevocable. The goal is to minimize both the number of centers and the $k$-means cost. Previous works in this setting assume that the input's order is random, or that the input's aspect ratio is bounded. It is known that if the order is arbitrary and there is no assumption on the input, then any algorithm must take all points as centers. Moreover, assuming a bounded aspect ratio is too restrictive -- it does not include natural input generated from mixture models. We introduce a new complexity measure that quantifies the difficulty of clustering a dataset arriving in arbitrary order. We design a new random algorithm and prove that if applied on data with complexity $d$, the algorithm takes $O(d\log(n) k\log(k))$ centers and is an $O(k^3)$-approximation. We also prove that if the data is sampled from a ``natural" distribution, such as a mixture of $k$ Gaussians, then the new complexity measure is equal to $O(k^2\log(n))$. This implies that for data generated from those distributions, our new algorithm takes only $\text{poly}(k\log(n))$ centers and is a $\text{poly}(k)$-approximation. In terms of negative results, we prove that the number of centers needed to achieve an $\alpha$-approximation is at least $\Omega\left(\frac{d}{k\log(n\alpha)}\right)$.