Konstantina Bairaktari

Konstantina Bairaktari, Guy Blanc, Li-Yang Tan et al. · berkeley

We investigate the computational efficiency of multitask learning of Boolean functions over the $d$-dimensional hypercube, that are related by means of a feature representation of size $k \ll d$ shared across all tasks. We present a polynomial time multitask learning algorithm for the concept class of halfspaces with margin $γ$, which is based on a simultaneous boosting technique and requires only $\textrm{poly}(k/γ)$ samples-per-task and $\textrm{poly}(k\log(d)/γ)$ samples in total. In addition, we prove a computational separation, showing that assuming there exists a concept class that cannot be learned in the attribute-efficient model, we can construct another concept class such that can be learned in the attribute-efficient model, but cannot be multitask learned efficiently -- multitask learning this concept class either requires super-polynomial time complexity or a much larger total number of samples.

Konstantina Bairaktari, Lunjia Hu, Huy L. Nguyen et al.

AI generated predictions increasingly inform decision making in critical tasks, and therefore must be trustworthy. One widely used measure of trustworthiness is calibration, which requires that the predictions match the true frequencies and can be treated like real probabilities of a given outcome. However, defining calibration is subtle, and designing good measures of calibration error has been an active topic of recent research. The first goal is to find calibration measures that are actionable, meaning they can inform decision makers about their utility loss when predictions are treated as true probabilities, which is known as swap regret. The second goal is to find calibration measures that are testable, meaning that calibration error can be measured from a small sample of predictions and outcomes. Although these are very basic requirements, there is no existing calibration measure that fully satisfies both properties, and all existing measures relax actionability by bounding a weaker notion of swap regret, or relax testability by having suboptimal estimation error. We introduce a new calibration measure, Soft-Binned Calibration Decision Loss (SCDL), which we prove is fully actionable without weakening either requirement, and testable with nearly optimal error rate. In addition, SCDL satisfies other desired properties such as continuity and consistency. We also provide a set of experiments confirming that the theoretical advantages of SCDL compared to other measures lead to better performance in practice.

Maryam Aliakbarpour, Konstantina Bairaktari, Gavin Brown et al.

Metalearning and multitask learning are two frameworks for solving a group of related learning tasks more efficiently than we could hope to solve each of the individual tasks on their own. In multitask learning, we are given a fixed set of related learning tasks and need to output one accurate model per task, whereas in metalearning we are given tasks that are drawn i.i.d. from a metadistribution and need to output some common information that can be easily specialized to new tasks from the metadistribution. We consider a binary classification setting where tasks are related by a shared representation, that is, every task $P$ can be solved by a classifier of the form $f_{P} \circ h$ where $h \in H$ is a map from features to a representation space that is shared across tasks, and $f_{P} \in F$ is a task-specific classifier from the representation space to labels. The main question we ask is how much data do we need to metalearn a good representation? Here, the amount of data is measured in terms of the number of tasks $t$ that we need to see and the number of samples $n$ per task. We focus on the regime where $n$ is extremely small. Our main result shows that, in a distribution-free setting where the feature vectors are in $\mathbb{R}^d$, the representation is a linear map from $\mathbb{R}^d \to \mathbb{R}^k$, and the task-specific classifiers are halfspaces in $\mathbb{R}^k$, we can metalearn a representation with error $\varepsilon$ using $n = k+2$ samples per task, and $d \cdot (1/\varepsilon)^{O(k)}$ tasks. Learning with so few samples per task is remarkable because metalearning would be impossible with $k+1$ samples per task, and because we cannot even hope to learn an accurate task-specific classifier with $k+2$ samples per task. Our work also yields a characterization of distribution-free multitask learning and reductions between meta and multitask learning.

Konstantina Bairaktari, Jiayun Wu, Zhiwei Steven Wu

Conformal prediction is a powerful distribution-free framework for constructing prediction sets with coverage guarantees. Classical methods, such as split conformal prediction, provide marginal coverage, ensuring that the prediction set contains the label of a random test point with a target probability. However, these guarantees may not hold uniformly across different subpopulations, leading to disparities in coverage. Prior work has explored coverage guarantees conditioned on events related to the covariates and label of the test point. We present Kandinsky conformal prediction, a framework that significantly expands the scope of conditional coverage guarantees. In contrast to Mondrian conformal prediction, which restricts its coverage guarantees to disjoint groups -- reminiscent of the rigid, structured grids of Piet Mondrian's art -- our framework flexibly handles overlapping and fractional group memberships defined jointly on covariates and labels, reflecting the layered, intersecting forms in Wassily Kandinsky's compositions. Our algorithm unifies and extends existing methods, encompassing covariate-based group conditional, class conditional, and Mondrian conformal prediction as special cases, while achieving a minimax-optimal high-probability conditional coverage bound. Finally, we demonstrate the practicality of our approach through empirical evaluation on real-world datasets.

Maryam Aliakbarpour, Konstantina Bairaktari, Adam Smith et al.

Model personalization allows a set of individuals, each facing a different learning task, to train models that are more accurate for each person than those they could develop individually. The goals of personalization are captured in a variety of formal frameworks, such as multitask learning and metalearning. Combining data for model personalization poses risks for privacy because the output of an individual's model can depend on the data of other individuals. In this work we undertake a systematic study of differentially private personalized learning. Our first main contribution is to construct a taxonomy of formal frameworks for private personalized learning. This taxonomy captures different formal frameworks for learning as well as different threat models for the attacker. Our second main contribution is to prove separations between the personalized learning problems corresponding to different choices. In particular, we prove a novel separation between private multitask learning and private metalearning.

Konstantina Bairaktari, Huy L. Nguyen

Calibrating a multiclass predictor, that outputs a distribution over labels, is particularly challenging due to the exponential number of possible prediction values. In this work, we propose a new definition of calibration error that interpolates between two established calibration error notions, one with known exponential sample complexity and one with polynomial sample complexity for calibrating a given predictor. Our algorithm can calibrate any given predictor for the entire range of interpolation, except for one endpoint, using only a polynomial number of samples. At the other endpoint, we achieve nearly optimal dependence on the error parameter, improving upon previous work. A key technical contribution is a novel application of adaptive data analysis with high adaptivity but only logarithmic overhead in the sample complexity.

Konstantina Bairaktari, Huy Le Nguyen, Jonathan Ullman

The rise of algorithmic decision-making has created an explosion of research around the fairness of those algorithms. While there are many compelling notions of individual fairness, beginning with the work of Dwork et al., these notions typically do not satisfy desirable composition properties. To this end, Dwork and Ilvento introduced the fair cohort selection problem, which captures a specific application where a single fair classifier is composed with itself to pick a group of candidates of size exactly $k$. In this work we introduce a specific instance of cohort selection where the goal is to choose a cohort maximizing a linear utility function. We give approximately optimal polynomial-time algorithms for this problem in both an offline setting where the entire fair classifier is given at once, or an online setting where candidates arrive one at a time and are classified as they arrive.

Konstantina Bairaktari, Paul Langton, Huy L. Nguyen et al.

A challenge in fair algorithm design is that, while there are compelling notions of individual fairness, these notions typically do not satisfy desirable composition properties, and downstream applications based on fair classifiers might not preserve fairness. To study fairness under composition, Dwork and Ilvento introduced an archetypal problem called fair-cohort-selection problem, where a single fair classifier is composed with itself to select a group of candidates of a given size, and proposed a solution to this problem. In this work we design algorithms for selecting cohorts that not only preserve fairness, but also maximize the utility of the selected cohort under two notions of utility that we introduce and motivate. We give optimal (or approximately optimal) polynomial-time algorithms for this problem in both an offline setting, and an online setting where candidates arrive one at a time and are classified as they arrive.