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Conformal prediction (CP) is a wrapper around traditional machine learning models, giving coverage guarantees under the sole assumption of exchangeability; in classification problems, a CP guarantees that the error rate is at most a chosen significance level, irrespective of whether the underlying model is misspecified. However, the prohibitive computational costs of full CP led researchers to design scalable alternatives, which alas do not attain the same guarantees or statistical power of full CP. In this paper, we use influence functions to efficiently approximate full CP. We prove that our method is a consistent approximation of full CP, and empirically show that the approximation error becomes smaller as the training set increases; e.g., for 1,000 training points the two methods output p-values that are <0.001 apart: a negligible error for any practical application. Our methods enable scaling full CP to large real-world datasets. We compare our full CP approximation (ACP) to mainstream CP alternatives, and observe that our method is computationally competitive whilst enjoying the statistical predictive power of full CP.
In this paper, we consider the parallel implementation of an already-trained deep model on multiple processing nodes (a.k.a. workers). Specifically, we investigate as to how a deep model should be divided into several parallel sub-models, each of which is executed efficiently by a worker. Since latency due to synchronization and data transfer among workers negatively impacts the performance of the parallel implementation, it is desirable to have minimum interdependency among parallel sub-models. To achieve this goal, we propose to rearrange the neurons in the neural network, partition them (without changing the general topology of the neural network), and modify the weights such that the interdependency among sub-models is minimized under the computations and communications constraints of the workers while minimizing its impact on the performance of the model. We propose RePurpose, a layer-wise model restructuring and pruning technique that guarantees the performance of the overall parallelized model. To efficiently apply RePurpose, we propose an approach based on L0 optimization and the Munkres assignment algorithm. We show that, compared to the existing methods, RePurpose significantly improves the efficiency of the distributed inference via parallel implementation, both in terms of communication and computational complexity.
One approach for interpreting black-box machine learning models is to find a global approximation of the model using simple interpretable functions, which is called a metamodel (a model of the model). Approximating the black-box with a metamodel can be used to 1) estimate instance-wise feature importance; 2) understand the functional form of the model; 3) analyze feature interactions. In this work, we propose a new method for finding interpretable metamodels. Our approach utilizes Kolmogorov superposition theorem, which expresses multivariate functions as a composition of univariate functions (our primitive parameterized functions). This composition can be represented in the form of a tree. Inspired by symbolic regression, we use a modified form of genetic programming to search over different tree configurations. Gradient descent (GD) is used to optimize the parameters of a given configuration. Our method is a novel memetic algorithm that uses GD not only for training numerical constants but also for the training of building blocks. Using several experiments, we show that our method outperforms recent metamodeling approaches suggested for interpreting black-boxes.
In reinforcement learning (RL), the ability to utilize prior knowledge from previously solved tasks can allow agents to quickly solve new problems. In some cases, these new problems may be approximately solved by composing the solutions of previously solved primitive tasks (task composition). Otherwise, prior knowledge can be used to adjust the reward function for a new problem, in a way that leaves the optimal policy unchanged but enables quicker learning (reward shaping). In this work, we develop a general framework for reward shaping and task composition in entropy-regularized RL. To do so, we derive an exact relation connecting the optimal soft value functions for two entropy-regularized RL problems with different reward functions and dynamics. We show how the derived relation leads to a general result for reward shaping in entropy-regularized RL. We then generalize this approach to derive an exact relation connecting optimal value functions for the composition of multiple tasks in entropy-regularized RL. We validate these theoretical contributions with experiments showing that reward shaping and task composition lead to faster learning in various settings.
Clustering with outliers is one of the most fundamental problems in Computer Science. Given a set X of n points and two numbers k and m, the clustering with outliers aims to exclude m points from X, and partition the remaining points into k clusters that minimizes a certain cost function. In this paper, we give a general approach for solving clustering with outliers, which results in a fixed-parameter tractable (FPT) algorithm in k and m (i.e., an algorithm with running time of the form f(k, m) * poly(n) for some function f), that almost matches the approximation ratio for its outlier-free counterpart. As a corollary, we obtain FPT approximation algorithms with optimal approximation ratios for k-Median and k-Means with outliers in general and Euclidean metrics. We also exhibit more applications of our approach to other variants of the problem that impose additional constraints on the clustering, such as fairness or matroid constraints.
Cross entropy loss has served as the main objective function for classification-based tasks. Widely deployed for learning neural network classifiers, it shows both effectiveness and a probabilistic interpretation. Recently, after the success of self supervised contrastive representation learning methods, supervised contrastive methods have been proposed to learn representations and have shown superior and more robust performance, compared to solely training with cross entropy loss. However, cross entropy loss is still needed to train the final classification layer. In this work, we investigate the possibility of learning both the representation and the classifier using one objective function that combines the robustness of contrastive learning and the probabilistic interpretation of cross entropy loss. First, we revisit a previously proposed contrastive-based objective function that approximates cross entropy loss and present a simple extension to learn the classifier jointly. Second, we propose a new version of the supervised contrastive training that learns jointly the parameters of the classifier and the backbone of the network. We empirically show that these proposed objective functions demonstrate state-of-the-art performance and show a significant improvement over the standard cross entropy loss with more training stability and robustness in various challenging settings.
Simulating physical network paths (e.g., Internet) is a cornerstone research problem in the emerging sub-field of AI-for-networking. We seek a model that generates end-to-end packet delay values in response to the time-varying load offered by a sender, which is typically a function of the previously output delays. The problem setting is unique, and renders the state-of-the-art text and time-series generative models inapplicable or ineffective. We formulate an ML problem at the intersection of dynamical systems, sequential decision making, and time-series modeling. We propose a novel grey-box approach to network simulation that embeds the semantics of physical network path in a new RNN-style model called Recurrent Buffering Unit, providing the interpretability of standard network simulator tools, the power of neural models, the efficiency of SGD-based techniques for learning, and yielding promising results on synthetic and real-world network traces.
We study fully dynamic online selection problems in an adversarial/stochastic setting that includes Bayesian online selection, prophet inequalities, posted price mechanisms, and stochastic probing problems subject to combinatorial constraints. In the classical ``incremental'' version of the problem, selected elements remain active until the end of the input sequence. On the other hand, in the fully dynamic version of the problem, elements stay active for a limited time interval, and then leave. This models, for example, the online matching of tasks to workers with task/worker-dependent working times, and sequential posted pricing of perishable goods. A successful approach to online selection problems in the adversarial setting is given by the notion of Online Contention Resolution Scheme (OCRS), that uses a priori information to formulate a linear relaxation of the underlying optimization problem, whose optimal fractional solution is rounded online for any adversarial order of the input sequence. Our main contribution is providing a general method for constructing an OCRS for fully dynamic online selection problems. Then, we show how to employ such OCRS to construct no-regret algorithms in a partial information model with semi-bandit feedback and adversarial inputs.
We study the problem of learning a hierarchical tree representation of data from labeled samples, taken from an arbitrary (and possibly adversarial) distribution. Consider a collection of data tuples labeled according to their hierarchical structure. The smallest number of such tuples required in order to be able to accurately label subsequent tuples is of interest for data collection in machine learning. We present optimal sample complexity bounds for this problem in several learning settings, including (agnostic) PAC learning and online learning. Our results are based on tight bounds of the Natarajan and Littlestone dimensions of the associated problem. The corresponding tree classifiers can be constructed efficiently in near-linear time.
We develop a meta-learning framework for simple regret minimization in bandits. In this framework, a learning agent interacts with a sequence of bandit tasks, which are sampled i.i.d. from an unknown prior distribution, and learns its meta-parameters to perform better on future tasks. We propose the first Bayesian and frequentist meta-learning algorithms for this setting. The Bayesian algorithm has access to a prior distribution over the meta-parameters and its meta simple regret over m bandit tasks with horizon n is mere O(m / √n). On the other hand, the meta simple regret of the frequentist algorithm is O(n√m + m/ √n). While its regret is worse, the frequentist algorithm is more general because it does not need a prior distribution over the meta-parameters. It can also be analyzed in more settings. We instantiate our algorithms for several classes of bandit problems. Our algorithms are general and we complement our theory by evaluating them empirically in several environments.
Downsampling produces coarsened, multi-resolution representations of data and it is used, for example, to produce lossy compression and visualization of large images, reduce computational costs, and boost deep neural representation learning. Unfortunately, due to their lack of a regular structure, there is still no consensus on how downsampling should apply to graphs and linked data. Indeed reductions in graph data are still needed for the goals described above, but reduction mechanisms do not have the same focus on preserving topological structures and properties, while allowing for resolution-tuning, as is the case in regular data downsampling. In this paper, we take a step in this direction, introducing a unifying interpretation of downsampling in regular and graph data. In particular, we define a graph coarsening mechanism which is a graph-structured counterpart of controllable equispaced coarsening mechanisms in regular data. We prove theoretical guarantees for distortion bounds on path lengths, as well as the ability to preserve key topological properties in the coarsened graphs. We leverage these concepts to define a graph pooling mechanism that we empirically assess in graph classification tasks, providing a greedy algorithm that allows efficient parallel implementation on GPUs, and showing that it compares favorably against pooling methods in literature.
Multi-task deep reinforcement learning (DRL) ambitiously aims to train a general agent that masters multiple tasks simultaneously. However, varying learning speeds of different tasks compounding with negative gradients interference makes policy learning inefficient. In this work, we propose PiCor, an efficient multi-task DRL framework that splits learning into policy optimization and policy correction phases. The policy optimization phase improves the policy by any DRL algothrim on the sampled single task without considering other tasks. The policy correction phase first constructs an adaptive adjusted performance constraint set. Then the intermediate policy learned by the first phase is constrained to the set, which controls the negative interference and balances the learning speeds across tasks. Empirically, we demonstrate that PiCor outperforms previous methods and significantly improves sample efficiency on simulated robotic manipulation and continuous control tasks. We additionally show that adaptive weight adjusting can further improve data efficiency and performance.
We consider the problem of constrained Markov decision process (CMDP) in continuous state actions spaces where the goal is to maximize the expected cumulative reward subject to some constraints. We propose a novel Conservative Natural Policy Gradient Primal Dual Algorithm (CNPGPD) to achieve zero constraint violation while achieving state of the art convergence results for the objective value function. For general policy parametrization, we prove convergence of value function to global optimal upto an approximation error due to restricted policy class. We improve the sample complexity of existing constrained NPGPD algorithm. To the best of our knowledge, this is the first work to establish zero constraint violation with Natural policy gradient style algorithms for infinite horizon discounted CMDPs. We demonstrate the merits of proposed algorithm via experimental evaluations.
Decision trees are widely used for their low computational cost, good predictive performance, and ability to assess the importance of features. Though often used in practice for feature selection, the theoretical guarantees of these methods are not well understood. We here obtain a tight finite sample bound for the feature selection problem in linear regression using single-depth decision trees. We examine the statistical properties of these "decision stumps" for the recovery of the s active features from p total features, where s << p. Our analysis provides tight sample performance guarantees on high-dimensional sparse systems which align with the finite sample bound of O(s log p) as obtained by Lasso, improving upon previous bounds for both the median and optimal splitting criteria. Our results extend to the non-linear regime as well as arbitrary sub-Gaussian distributions, demonstrating that tree based methods attain strong feature selection properties under a wide variety of settings and further shedding light on the success of these methods in practice. As a byproduct of our analysis, we show that we can provably guarantee recovery even when the number of active features s is unknown. We further validate our theoretical results and proof methodology using computational experiments.
Our work targets at searching feasible adversarial perturbation to attack a classifier with high-dimensional categorical inputs in a domain-agnostic setting. This is intrinsically a NP-hard knapsack problem where the exploration space becomes explosively larger as the feature dimension increases. Without the help of domain knowledge, solving this problem via heuristic method, such as Branch-and-Bound, suffers from exponential complexity, yet can bring arbitrarily bad attack results. We address the challenge via the lens of multi-armed bandit based combinatorial search. Our proposed method, namely FEAT, treats modifying each categorical feature as pulling an arm in multi-armed bandit programming. Our objective is to achieve highly efficient and effective attack using an Orthogonal Matching Pursuit (OMP)-enhanced Upper Confidence Bound (UCB) exploration strategy. Our theoretical analysis bounding the regret gap of FEAT guarantees its practical attack performance. In empirical analysis, we compare FEAT with other state-of-the-art domain-agnostic attack methods over various real-world categorical data sets of different applications. Substantial experimental observations confirm the expected efficiency and attack effectiveness of FEAT applied in different application scenarios. Our work further hints the applicability of FEAT for assessing the adversarial vulnerability of classification systems with high-dimensional categorical inputs.
We extend the notion of regret with a welfarist perspective. Focussing on the classic multi-armed bandit (MAB) framework, the current work quantifies the performance of bandit algorithms by applying a fundamental welfare function, namely the Nash social welfare (NSW) function. This corresponds to equating algorithm's performance to the geometric mean of its expected rewards and leads us to the study of Nash regret, defined as the difference between the - a priori unknown - optimal mean (among the arms) and the algorithm's performance. Since NSW is known to satisfy fairness axioms, our approach complements the utilitarian considerations of average (cumulative) regret, wherein the algorithm is evaluated via the arithmetic mean of its expected rewards. This work develops an algorithm that, given the horizon of play T, achieves a Nash regret of O ( sqrt{(k log T)/T} ), here k denotes the number of arms in the MAB instance. Since, for any algorithm, the Nash regret is at least as much as its average regret (the AM-GM inequality), the known lower bound on average regret holds for Nash regret as well. Therefore, our Nash regret guarantee is essentially tight. In addition, we develop an anytime algorithm with a Nash regret guarantee of O( sqrt{(k log T)/T} log T ).
Variational quantum algorithms (VQAs) are the quantum analog of classical neural networks (NNs). A VQA consists of a parameterized quantum circuit (PQC) which is composed of multiple layers of ansatzes (simpler PQCs, which are an analogy of NN layers) that differ only in selections of parameters. Previous work has identified the alternating layered ansatz as potentially a new standard ansatz in near-term quantum computing. Indeed, shallow alternating layered VQAs are easy to implement and have been shown to be both trainable and expressive. In this work, we introduce a training algorithm with an exponential reduction in training cost of such VQAs. Moreover, our algorithm uses classical shadows of quantum input data, and can hence be run on a classical computer with rigorous performance guarantees. We demonstrate 2-3 orders of magnitude improvement in the training cost using our algorithm for the example problems of finding state preparation circuits and the quantum autoencoder.
Learning on evolving(dynamic) graphs has caught the attention of researchers as static methods exhibit limited performance in this setting. The existing methods for dynamic graphs learn spatial features by local neighborhood aggregation, which essentially only captures the low pass signals and local interactions. In this work, we go beyond current approaches to incorporate global features for effectively learning representations of a dynamically evolving graph. We propose to do so by capturing the spectrum of the dynamic graph. Since static methods to learn the graph spectrum would not consider the history of the evolution of the spectrum as the graph evolves with time, we propose an approach to learn the graph wavelets to capture this evolving spectra. Further, we propose a framework that integrates the dynamically captured spectra in the form of these learnable wavelets into spatial features for incorporating local and global interactions. Experiments on eight standard datasets show that our method significantly outperforms related methods on various tasks for dynamic graphs.
We introduce equi-tuning, a novel fine-tuning method that transforms (potentially non-equivariant) pretrained models into group equivariant models while incurring minimum L_2 loss between the feature representations of the pretrained and the equivariant models. Large pretrained models can be equi-tuned for different groups to satisfy the needs of various downstream tasks. Equi-tuned models benefit from both group equivariance as an inductive bias and semantic priors from pretrained models. We provide applications of equi-tuning on three different tasks: image classification, compositional generalization in language, and fairness in natural language generation (NLG). We also provide a novel group-theoretic definition for fairness in NLG. The effectiveness of this definition is shown by testing it against a standard empirical method of fairness in NLG. We provide experimental results for equi-tuning using a variety of pretrained models: Alexnet, Resnet, VGG, and Densenet for image classification; RNNs, GRUs, and LSTMs for compositional generalization; and GPT2 for fairness in NLG. We test these models on benchmark datasets across all considered tasks to show the generality and effectiveness of the proposed method.
Machine learning systems are often deployed for making critical decisions like credit lending, hiring, etc. While making decisions, such systems often encode the user's demographic information (like gender, age) in their intermediate representations. This can lead to decisions that are biased towards specific demographics. Prior work has focused on debiasing intermediate representations to ensure fair decisions. However, these approaches fail to remain fair with changes in the task or demographic distribution. To ensure fairness in the wild, it is important for a system to adapt to such changes as it accesses new data in an incremental fashion. In this work, we propose to address this issue by introducing the problem of learning fair representations in an incremental learning setting. To this end, we present Fairness-aware Incremental Representation Learning (FaIRL), a representation learning system that can sustain fairness while incrementally learning new tasks. FaIRL is able to achieve fairness and learn new tasks by controlling the rate-distortion function of the learned representations. Our empirical evaluations show that FaIRL is able to make fair decisions while achieving high performance on the target task, outperforming several baselines.
In this work, we demonstrate how to reliably estimate epistemic uncertainty while maintaining the flexibility needed to capture complicated aleatoric distributions. To this end, we propose an ensemble of Normalizing Flows (NF), which are state-of-the-art in modeling aleatoric uncertainty. The ensembles are created via sets of fixed dropout masks, making them less expensive than creating separate NF models. We demonstrate how to leverage the unique structure of NFs, base distributions, to estimate aleatoric uncertainty without relying on samples, provide a comprehensive set of baselines, and derive unbiased estimates for differential entropy. The methods were applied to a variety of experiments, commonly used to benchmark aleatoric and epistemic uncertainty estimation: 1D sinusoidal data, 2D windy grid-world (Wet Chicken), Pendulum, and Hopper. In these experiments, we setup an active learning framework and evaluate each model's capability at measuring aleatoric and epistemic uncertainty. The results show the advantages of using NF ensembles in capturing complicated aleatoric while maintaining accurate epistemic uncertainty estimates.
We study a fundamental model of online preference aggregation, where an algorithm maintains an ordered list of n elements. An input is a stream of preferred sets R_1, R_2, ..., R_t, ... Upon seeing R_t and without knowledge of any future sets, an algorithm has to rerank elements (change the list ordering), so that at least one element of R_t is found near the list front. The incurred cost is a sum of the list update costs (the number of swaps of neighboring list elements) and access cost (the position of the first element of R_t on the list). This scenario occurs naturally in applications such as ordering items in an online shop using aggregated preferences of shop customers. The theoretical underpinning of this problem is known as Min-Sum Set Cover. Unlike previous work that mostly studied the performance of an online algorithm ALG in comparison to the static optimal solution (a single optimal list ordering), in this paper, we study an arguably harder variant where the benchmark is the provably stronger optimal dynamic solution OPT (that may also modify the list ordering). In terms of an online shop, this means that the aggregated preferences of its user base evolve with time. We construct a computationally efficient randomized algorithm whose competitive ratio (ALG-to-OPT cost ratio) is O(r^2) and prove the existence of a deterministic O(r^4)-competitive algorithm. Here, r is the maximum cardinality of sets R_t. This is the first algorithm whose ratio does not depend on n: the previously best algorithm for this problem was O(r^(3/2) * n^(1/2))-competitive and Ω(r) is a lower bound on the performance of any deterministic online algorithm.
Neural networks require careful weight initialization to prevent signals from exploding or vanishing. Existing initialization schemes solve this problem in specific cases by assuming that the network has a certain activation function or topology. It is difficult to derive such weight initialization strategies, and modern architectures therefore often use these same initialization schemes even though their assumptions do not hold. This paper introduces AutoInit, a weight initialization algorithm that automatically adapts to different neural network architectures. By analytically tracking the mean and variance of signals as they propagate through the network, AutoInit appropriately scales the weights at each layer to avoid exploding or vanishing signals. Experiments demonstrate that AutoInit improves performance of convolutional, residual, and transformer networks across a range of activation function, dropout, weight decay, learning rate, and normalizer settings, and does so more reliably than data-dependent initialization methods. This flexibility allows AutoInit to initialize models for everything from small tabular tasks to large datasets such as ImageNet. Such generality turns out particularly useful in neural architecture search and in activation function discovery. In these settings, AutoInit initializes each candidate appropriately, making performance evaluations more accurate. AutoInit thus serves as an automatic configuration tool that makes design of new neural network architectures more robust. The AutoInit package provides a wrapper around TensorFlow models and is available at https://github.com/cognizant-ai-labs/autoinit.
Probably Approximately Correct (i.e., PAC) learning is a core concept of sample complexity theory, and efficient PAC learnability is often seen as a natural counterpart to the class P in classical computational complexity. But while the nascent theory of parameterized complexity has allowed us to push beyond the P-NP "dichotomy" in classical computational complexity and identify the exact boundaries of tractability for numerous problems, there is no analogue in the domain of sample complexity that could push beyond efficient PAC learnability. As our core contribution, we fill this gap by developing a theory of parameterized PAC learning which allows us to shed new light on several recent PAC learning results that incorporated elements of parameterized complexity. Within the theory, we identify not one but two notions of fixed-parameter learnability that both form distinct counterparts to the class FPT - the core concept at the center of the parameterized complexity paradigm - and develop the machinery required to exclude fixed-parameter learnability. We then showcase the applications of this theory to identify refined boundaries of tractability for CNF and DNF learning as well as for a range of learning problems on graphs.
We develop the first fully dynamic algorithm that maintains a decision tree over an arbitrary sequence of insertions and deletions of labeled examples. Given ε>0 our algorithm guarantees that, at every point in time, every node of the decision tree uses a split with Gini gain within an additive ε of the optimum. For real-valued features the algorithm has an amortized running time per insertion/deletion of O((d·log³n)/ε²), which improves to O((d·log²n)/ε) for binary or categorical features, while it uses space O(n·d), where n is the maximum number of examples at any point in time and d is the number of features. Our algorithm is nearly optimal, as we show that any algorithm with similar guarantees requires amortized running time Ω(d) and space Ω(n·d/polylog(nd)). We complement our theoretical results with an extensive experimental evaluation on real-world data, showing the effectiveness of our algorithm.