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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 &quot;dichotomy&quot; 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.

AAAI 2023

A Parameterized Theory of PAC Learning

ml: reinforcement learning theory

krr: computational complexity of reasoning

ml: learning theory

The purpose of the AAAI conference series is to promote research in Artificial Intelligence (AI) and foster scientific exchange between researchers, practitioners, scientists, students, and engineers across the entirety of AI and its affiliated disciplines. AAAI-23 is the Thirty-Seventh AAAI Conference on Artificial Intelligence. The theme of this conference is to create collaborative bridges within and beyond AI. Like previous AAAI conferences, AAAI-23 will feature technical paper presentations, special tracks, invited speakers, workshops, tutorials, poster sessions, senior member presentations, competitions, and exhibit programs, and two new activities: a Bridge Program and a Lab Program. Many of these activities are tailored to the theme of bridges and all are selected according to the highest standards, with additional programs for students and young researchers. 
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The purpose of the AAAI conference series is to promote research in Artificial Intelligence (AI) and foster scientific exchange between researchers, practitioners, scientists, students, and engineers across the entirety of AI and its affiliated disciplines.

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.

poster

Knowledge graph embedding (KGE), which maps entities and relations in a knowledge graph into continuous vector spaces, has achieved great success in predicting missing links in knowledge graphs. However, knowledge graphs often contain incomplete triples that are difficult to inductively infer by KGEs. To address this challenge, we resort to analogical inference and propose a novel and general self-supervised framework AnKGE to enhance KGE models with analogical inference capability. We propose an analogical object retriever that retrieves appropriate analogical objects from entity-level, relation-level, and triple-level. And in AnKGE, we train an analogy function for each level of analogical inference with the original element embedding from a well-trained KGE model as input, which outputs the analogical object embedding. In order to combine inductive inference capability from the original KGE model and analogical inference capability enhanced by AnKGE, we interpolate the analogy score with the base model score and introduce the adaptive weights in the score function for prediction. Through extensive experiments on FB15k-237 and WN18RR datasets, we show that AnKGE achieves competitive results on link prediction task and well performs analogical inference. 

Analogical Inference Enhanced Knowledge Graph Embedding

Most current Artificial Intelligence applications are based on supervised Machine Learning (ML), which ultimately grounds on data annotated by small teams of experts or large ensemble of volunteers. The annotation process is often performed in terms of a majority vote, however this has been proved to be often problematic by recent evaluation studies.
In this article, we describe and advocate for a different paradigm, which we call \emph{perspectivism}: this counters the removal of disagreement and, consequently, the assumption of correctness of traditionally aggregated gold-standard datasets, and proposes the adoption of methods that \emph{preserve} divergence of opinions and integrate multiple perspectives in the ground truthing process of ML development. Drawing on previous works which inspired it, mainly from the crowdsourcing and multi-rater labeling settings, we survey the state-of-the-art and describe the potential of our proposal for not only the more subjective tasks (e.g. those related to human language) but also those tasks commonly understood as objective (e.g. medical decision making). We present the main benefits of adopting a perspectivist stance in ML, as well as possible disadvantages, and various ways in which such a stance can be implemented in practice. Finally, we share a set of recommendations and outline a research agenda to advance the perspectivist stance in ML.

Toward a Perspectivist Turn in Ground Truthing for Predictive Computing

Image clustering is an important and open challenging task in computer vision. Although many methods have been proposed to solve the image clustering task, they only explore images and uncover clusters according to the image features, thus being unable to distinguish visually similar but semantically different images. In this paper, we propose to investigate the task of image clustering with the help of visual-language pre-training model. Different from the zero-shot setting, in which the class names are known, we only know the number of clusters in this setting. Therefore, how to map images to a proper semantic space and how to cluster images from both image and semantic spaces are two key problems. To solve the above problems, we propose a novel image clustering method guided by the visual-language pre-training model CLIP, named \textbf{Semantic-enhanced Image Clustering (SIC)}. In this new method, we propose a method to map the given images to a proper semantic space first and efficient methods to generate pseudo-labels according to the relationships between images and semantics. Finally, we propose to perform clustering with consistency learning in both image space and semantic space, in a self-supervised learning fashion. The theoretical result of convergence analysis shows that our proposed method can converge at a sublinear speed. Theoretical analysis of expectation risk also shows that we can reduce the expectation risk by improving neighborhood consistency, increasing prediction confidence, or reducing neighborhood imbalance. Experimental results on five benchmark datasets clearly show the superiority of our new method.

Semantic-enhanced Image Clustering

Understanding temporal commonsense concepts, such as times of occurrence and durations is crucial for event-centric language understanding. Reasoning about such temporal concepts in a complex context requires reasoning over both the stated context and the world knowledge that underlines it. A recent study shows massive pre-trained LM still struggle with such temporal reasoning under complex contexts (e.g., dialog) because they only implicitly encode the relevant contexts and fail to explicitly uncover the underlying logical compositions for complex inference, thus may not be robust enough. In this work, we propose to augment LMs with the temporal logic induction ability, which frames the temporal reasoning by defining three modular components: temporal dependency inducer and temporal concept defuzzifier and logic validator. The former two components disentangle the explicit/implicit dependency between temporal concepts across context (before, after, ...) and the specific meaning of fuzzy temporal concepts, respectively, while the validator combines the intermediate reasoning clues for robust contextual reasoning about the temporal concepts. Extensive experimental results on TIMEDIAL, a challenging dataset for temporal reasoning over dialog, show that our method, Logic Induction Enhanced Contextualized TEmporal Reasoning (LECTER), can yield great improvements over the traditional language model for temporal reasoning.

Self-supervised Logic Induction for Explainable Fuzzy Temporal Commonsense Reasoning

We study the close interplay between error and compression in the non-parametric multiclass classification setting in terms of prototype learning rules. We focus in particular on a recently proposed compression-based learning rule termed OptiNet. Beyond its computational merits, this rule has been recently shown to be universally consistent in any metric instance space that admits a universally consistent rule---the first learning algorithm known to enjoy this property. However, its error and compression rates have been left open. Here we derive such rates in the case where instances reside in Euclidean space under commonly posed smoothness and tail conditions on the data distribution. We first show that OptiNet achieves non-trivial compression rates while enjoying near minimax-optimal error rates. We then proceed to study a novel general compression scheme for further compressing prototype rules that locally adapts to the noise level without sacrificing accuracy. Applying it to OptiNet, we show that under a geometric margin condition further gain in the compression rate is achieved. Experimental results comparing the performance of the various methods are presented.

On Error and Compression Rates for Prototype Rules

The problem of covariate-shift generalization has attracted intensive research attention. Previous stable learning algorithms employ sample reweighting schemes to decorrelate the covariates when there is no explicit domain information about training data. However, with finite samples, it is difficult to achieve the desirable weights that ensure perfect independence to get rid of the unstable variables. Besides, decorrelating within stable variables may bring about high variance of learned models because of the over-reduced effective sample size. A tremendous sample size is required for these algorithms to work. In this paper, with theoretical justification, we propose SVI (Sparse Variable Independence) for the covariate-shift generalization problem. We introduce sparsity constraint to compensate for the imperfectness of sample reweighting under the finite-sample setting in previous methods. Furthermore, we organically combine independence-based sample reweighting and sparsity-based variable selection in an iterative way to avoid decorrelating within stable variables, increasing the effective sample size to alleviate variance inflation. Experiments on both synthetic and real-world datasets demonstrate the improvement of covariate-shift generalization performance brought by SVI. 

Stable Learning via Sparse Variable Independence

Standard deep reinforcement learning (DRL) aims to maximize expected reward, considering collected experiences equally in formulating a policy. This differs from human decision-making, where gains and losses are valued differently and outlying outcomes are given increased consideration.  It also fails to capitalize on opportunities to improve safety and/or performance through the incorporation of distributional context. Several approaches to distributional DRL have been investigated, with one popular strategy being to evaluate the projected distribution of returns for possible actions.  We propose a more direct approach whereby risk-sensitive objectives, specified in terms of the cumulative distribution function (CDF) of the distribution of full-episode rewards, are optimized. This approach allows for outcomes to be weighed based on relative quality, can be used for both continuous and discrete action spaces, and may naturally be applied in both constrained and unconstrained settings.  We show how to compute an asymptotically consistent estimate of the policy gradient for a broad class of risk-sensitive objectives via sampling, subsequently incorporating variance reduction and regularization measures to facilitate effective on-policy learning.  We then demonstrate that the use of moderately "pessimistic" risk profiles, which emphasize scenarios where the agent performs poorly, leads to enhanced exploration and a continual focus on addressing deficiencies.  We test the approach using different risk profiles in six OpenAI Safety Gym environments, comparing to state of the art on-policy methods.  Without cost constraints, we find that pessimistic risk profiles can be used to reduce cost while improving total reward accumulation.  With cost constraints, they are seen to provide higher positive rewards than risk-neutral approaches at the prescribed allowable cost.

A Risk-Sensitive Approach to Policy Optimization

Deepfake brings huge and potential negative impacts to our daily lives. As the real-life Deepfake videos circulated on the Internet become more authentic, most existing detection algorithms have failed since few visual differences can be observed between an authentic video and a Deepfake one. However, the forensic traces are always retained within the synthesized videos. In this study, we present a noise-based Deepfake detection model, NoiseDF for short, which focuses on the underlying forensic noise traces left behind the Deepfake videos. In particular, we enhance the RIDNet denoiser to extract noise traces and features from the cropped face and background squares of the video image frames. Meanwhile, we devise a novel Multi-Head Relative-Interaction method to evaluate the degree of interaction between the faces and backgrounds that plays a pivotal role in the Deepfake detection task. Besides outperforming the state-of-the-art models, the visualization of the extracted Deepfake forensic noise traces has further displayed the evidence and proved the robustness of our approach.

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A Parameterized Theory of PAC Learning

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