OpenRaiser/Intern-Atlas huggingface dataset:
Breaking the Sample Size Barrier in Model-Based Reinforcement Learning with a Generative Model
Venue: arXiv cs.LG 2023
Year: 2023

This paper is concerned with the sample efficiency of reinforcement learning, assuming access to a generative model (or simulator). We first consider $γ$-discounted infinite-horizon Markov decision processes (MDPs) with state space $\mathcal{S}$ and action space $\mathcal{A}$. Despite a number of prior works tackling this problem, a complete picture of the trade-offs between sample complexity and statistical accuracy is yet to be determined. In particular, all prior results suffer from a severe sample size barrier, in the sense that their claimed statistical guarantees hold only when the sample size exceeds at least $\frac{|\mathcal{S}||\mathcal{A}|}{(1-γ)^2}$. The current paper overcomes this barrier by certifying the minimax optimality of two algorithms -- a perturbed model-based algorithm and a conservative model-based algorithm -- as soon as the sample size exceeds the order of $\frac{|\mathcal{S}||\mathcal{A}|}{1-γ}$ (modulo some log factor). Moving beyond infinite-horizon MDPs, we further study time-inhomogeneous finite-horizon MDPs, and prove that a plain model-based planning algorithm suffices to achieve minimax-optimal sample complexity given any target accuracy level. To the best of our knowledge, this work delivers the first minimax-optimal guarantees that accommodate the entire range of sample sizes (beyond which finding a meaningful policy is information theoretically infeasible).
Aperiodicity, Star-freeness, and First-order Logic Definability of Operator Precedence Languages
Venue: arXiv cs.FL 2023
Year: 2023

A classic result in formal language theory is the equivalence among non-counting, or aperiodic, regular languages, and languages defined through star-free regular expressions, or first-order logic. Past attempts to extend this result beyond the realm of regular languages have met with difficulties: for instance it is known that star-free tree languages may violate the non-counting property and there are aperiodic tree languages that cannot be defined through first-order logic. We extend such classic equivalence results to a significant family of deterministic context-free languages, the operator-precedence languages (OPL), which strictly includes the widely investigated visibly pushdown, alias input-driven, family and other structured context-free languages. The OP model originated in the '60s for defining programming languages and is still used by high performance compilers; its rich algebraic properties have been investigated initially in connection with grammar learning and recently completed with further closure properties and with monadic second order logic definition. We introduce an extension of regular expressions, the OP-expressions (OPE) which define the OPLs and, under the star-free hypothesis, define first-order definable and non-counting OPLs. Then, we prove, through a fairly articulated grammar transformation, that aperiodic OPLs are first-order definable. Thus, the classic equivalence of star-freeness, aperiodicity, and first-order definability is established for the large and powerful class of OPLs. We argue that the same approach can be exploited to obtain analogous results for visibly pushdown languages too.
Deep Learning Methods for Real-time Detection and Analysis of Wagner Ulcer Classification System
Venue: arXiv cs.CV 2023
Year: 2023

At present, the ubiquity method to diagnose the severity of diabetic feet (DF) depends on professional podiatrists. However, in most cases, professional podiatrists have a heavy workload, especially in underdeveloped and developing countries and regions, and there are often insufficient podiatrists to meet the rapidly growing treatment needs of DF patients. It is necessary to develop a medical system that assists in diagnosing DF in order to reduce part of the workload for podiatrists and to provide timely relevant information to patients with DF. In this paper, we have developed a system that can classify and locate Wagner ulcers of diabetic foot in real-time. First, we proposed a dataset of 2688 diabetic feet with annotations. Then, in order to enable the system to detect diabetic foot ulcers in real time and accurately, this paper is based on the YOLOv3 algorithm coupled with image fusion, label smoothing, and variant learning rate mode technologies to improve the robustness and predictive accuracy of the original algorithm. Finally, the refinements on YOLOv3 was used as the optimal algorithm in this paper to deploy into Android smartphone to predict the classes and localization of the diabetic foot with real-time. The experimental results validate that the improved YOLOv3 algorithm achieves a mAP of 91.95%, and meets the needs of real-time detection and analysis of diabetic foot Wagner Ulcer on mobile devices, such as smart phones. This work has the potential to lead to a paradigm shift for clinical treatment of the DF in the future, to provide an effective healthcare solution for DF tissue analysis and healing status.
Fully Dynamic Algorithm for Constrained Submodular Optimization
Venue: arXiv cs.DS 2023
Year: 2023

The task of maximizing a monotone submodular function under a cardinality constraint is at the core of many machine learning and data mining applications, including data summarization, sparse regression and coverage problems. We study this classic problem in the fully dynamic setting, where elements can be both inserted and removed. Our main result is a randomized algorithm that maintains an efficient data structure with a poly-logarithmic amortized update time and yields a $(1/2-ε)$-approximate solution. We complement our theoretical analysis with an empirical study of the performance of our algorithm.
Conditional Sig-Wasserstein GANs for Time Series Generation
Venue: arXiv cs.LG 2023
Year: 2023

Generative adversarial networks (GANs) have been extremely successful in generating samples, from seemingly high dimensional probability measures. However, these methods struggle to capture the temporal dependence of joint probability distributions induced by time-series data. Furthermore, long time-series data streams hugely increase the dimension of the target space, which may render generative modelling infeasible. To overcome these challenges, motivated by the autoregressive models in econometric, we are interested in the conditional distribution of future time series given the past information. We propose the generic conditional Sig-WGAN framework by integrating Wasserstein-GANs (WGANs) with mathematically principled and efficient path feature extraction called the signature of a path. The signature of a path is a graded sequence of statistics that provides a universal description for a stream of data, and its expected value characterises the law of the time-series model. In particular, we develop the conditional Sig-$W_1$ metric, that captures the conditional joint law of time series models, and use it as a discriminator. The signature feature space enables the explicit representation of the proposed discriminators which alleviates the need for expensive training. We validate our method on both synthetic and empirical dataset and observe that our method consistently and significantly outperforms state-of-the-art benchmarks with respect to measures of similarity and predictive ability.
Novelty Detection via Robust Variational Autoencoding
Venue: arXiv cs.LG 2023
Year: 2023

We propose a new method for novelty detection that can tolerate high corruption of the training points, whereas previous works assumed either no or very low corruption. Our method trains a robust variational autoencoder (VAE), which aims to generate a model for the uncorrupted training points. To gain robustness to high corruption, we incorporate the following four changes to the common VAE: 1. Extracting crucial features of the latent code by a carefully designed dimension reduction component for distributions; 2. Modeling the latent distribution as a mixture of Gaussian low-rank inliers and full-rank outliers, where the testing only uses the inlier model; 3. Applying the Wasserstein-1 metric for regularization, instead of the Kullback-Leibler (KL) divergence; and 4. Using a robust error for reconstruction. We establish both robustness to outliers and suitability to low-rank modeling of the Wasserstein metric as opposed to the KL divergence. We illustrate state-of-the-art results on standard benchmarks.
On Low Rank Directed Acyclic Graphs and Causal Structure Learning
Venue: arXiv cs.LG 2023
Year: 2023

Despite several advances in recent years, learning causal structures represented by directed acyclic graphs (DAGs) remains a challenging task in high dimensional settings when the graphs to be learned are not sparse. In this paper, we propose to exploit a low rank assumption regarding the (weighted) adjacency matrix of a DAG causal model to help address this problem. We utilize existing low rank techniques to adapt causal structure learning methods to take advantage of this assumption and establish several useful results relating interpretable graphical conditions to the low rank assumption. Specifically, we show that the maximum rank is highly related to hubs, suggesting that scale-free networks, which are frequently encountered in practice, tend to be low rank. Our experiments demonstrate the utility of the low rank adaptations for a variety of data models, especially with relatively large and dense graphs. Moreover, with a validation procedure, the adaptations maintain a superior or comparable performance even when graphs are not restricted to be low rank.
Ansor: Generating High-Performance Tensor Programs for Deep Learning
Venue: arXiv cs.LG 2023
Year: 2023

High-performance tensor programs are crucial to guarantee efficient execution of deep neural networks. However, obtaining performant tensor programs for different operators on various hardware platforms is notoriously challenging. Currently, deep learning systems rely on vendor-provided kernel libraries or various search strategies to get performant tensor programs. These approaches either require significant engineering effort to develop platform-specific optimization code or fall short of finding high-performance programs due to restricted search space and ineffective exploration strategy. We present Ansor, a tensor program generation framework for deep learning applications. Compared with existing search strategies, Ansor explores many more optimization combinations by sampling programs from a hierarchical representation of the search space. Ansor then fine-tunes the sampled programs with evolutionary search and a learned cost model to identify the best programs. Ansor can find high-performance programs that are outside the search space of existing state-of-the-art approaches. In addition, Ansor utilizes a task scheduler to simultaneously optimize multiple subgraphs in deep neural networks. We show that Ansor improves the execution performance of deep neural networks relative to the state-of-the-art on the Intel CPU, ARM CPU, and NVIDIA GPU by up to $3.8\times$, $2.6\times$, and $1.7\times$, respectively.
Selecting the Number of Clusters $K$ with a Stability Trade-off: an Internal Validation Criterion
Venue: arXiv cs.LG 2023
Year: 2023

Model selection is a major challenge in non-parametric clustering. There is no universally admitted way to evaluate clustering results for the obvious reason that no ground truth is available. The difficulty to find a universal evaluation criterion is a consequence of the ill-defined objective of clustering. In this perspective, clustering stability has emerged as a natural and model-agnostic principle: an algorithm should find stable structures in the data. If data sets are repeatedly sampled from the same underlying distribution, an algorithm should find similar partitions. However, stability alone is not well-suited to determine the number of clusters. For instance, it is unable to detect if the number of clusters is too small. We propose a new principle: a good clustering should be stable, and within each cluster, there should exist no stable partition. This principle leads to a novel clustering validation criterion based on between-cluster and within-cluster stability, overcoming limitations of previous stability-based methods. We empirically demonstrate the effectiveness of our criterion to select the number of clusters and compare it with existing methods. Code is available at https://github.com/FlorentF9/skstab.
Constrained regret minimization for multi-criterion multi-armed bandits
Venue: arXiv cs.LG 2023
Year: 2023

We consider a stochastic multi-armed bandit setting and study the problem of constrained regret minimization over a given time horizon. Each arm is associated with an unknown, possibly multi-dimensional distribution, and the merit of an arm is determined by several, possibly conflicting attributes. The aim is to optimize a 'primary' attribute subject to user-provided constraints on other 'secondary' attributes. We assume that the attributes can be estimated using samples from the arms' distributions, and that the estimators enjoy suitable concentration properties. We propose an algorithm called Con-LCB that guarantees a logarithmic regret, i.e., the average number of plays of all non-optimal arms is at most logarithmic in the horizon. The algorithm also outputs a Boolean flag that correctly identifies, with high probability, whether the given instance is feasible/infeasible with respect to the constraints. We also show that Con-LCB is optimal within a universal constant, i.e., that more sophisticated algorithms cannot do much better universally. Finally, we establish a fundamental trade-off between regret minimization and feasibility identification. Our framework finds natural applications, for instance, in financial portfolio optimization, where risk constrained maximization of expected return is meaningful.
Explainable and Discourse Topic-aware Neural Language Understanding
Venue: arXiv cs.CL 2023
Year: 2023

Marrying topic models and language models exposes language understanding to a broader source of document-level context beyond sentences via topics. While introducing topical semantics in language models, existing approaches incorporate latent document topic proportions and ignore topical discourse in sentences of the document. This work extends the line of research by additionally introducing an explainable topic representation in language understanding, obtained from a set of key terms correspondingly for each latent topic of the proportion. Moreover, we retain sentence-topic associations along with document-topic association by modeling topical discourse for every sentence in the document. We present a novel neural composite language model that exploits both the latent and explainable topics along with topical discourse at sentence-level in a joint learning framework of topic and language models. Experiments over a range of tasks such as language modeling, word sense disambiguation, document classification, retrieval and text generation demonstrate ability of the proposed model in improving language understanding.
Newton-type Methods for Minimax Optimization
Venue: arXiv cs.LG 2023
Year: 2023

Differential games, in particular two-player sequential zero-sum games (a.k.a. minimax optimization), have been an important modeling tool in applied science and received renewed interest in machine learning due to many recent applications, such as adversarial training, generative models and reinforcement learning. However, existing theory mostly focuses on convex-concave functions with few exceptions. In this work, we propose two novel Newton-type algorithms for nonconvex-nonconcave minimax optimization. We prove their local convergence at strict local minimax points, which are surrogates of global solutions. We argue that our Newton-type algorithms nicely complement existing ones in that (a) they converge faster to strict local minimax points; (b) they are much more effective when the problem is ill-conditioned; (c) their computational complexity remains similar. We verify the effectiveness of our Newton-type algorithms through experiments on training GANs which are intrinsically nonconvex and ill-conditioned. Our code is available at https://github.com/watml/min-max-2nd-order.
Boosting Deep Neural Networks with Geometrical Prior Knowledge: A Survey
Venue: arXiv cs.CV 2023
Year: 2023

Deep Neural Networks achieve state-of-the-art results in many different problem settings by exploiting vast amounts of training data. However, collecting, storing and - in the case of supervised learning - labelling the data is expensive and time-consuming. Additionally, assessing the networks' generalization abilities or predicting how the inferred output changes under input transformations is complicated since the networks are usually treated as a black box. Both of these problems can be mitigated by incorporating prior knowledge into the neural network. One promising approach, inspired by the success of convolutional neural networks in computer vision tasks, is to incorporate knowledge about symmetric geometrical transformations of the problem to solve that affect the output in a predictable way. This promises an increased data efficiency and more interpretable network outputs. In this survey, we try to give a concise overview about different approaches that incorporate geometrical prior knowledge into neural networks. Additionally, we connect those methods to 3D object detection for autonomous driving, where we expect promising results when applying those methods.
Scattered one-counter languges have rank less than $ω^2$
Venue: arXiv cs.FL 2023
Year: 2023

A linear ordering is called context-free if it is the lexicographic ordering of some context-free language and is called scattered if it has no dense subordering. Each scattered ordering has an associated ordinal, called its rank. It is known that scattered context-free (regular, resp.) orderings have rank less than $ω^ω$ ($ω$, resp). In this paper we confirm the conjecture that one-counter languages have rank less than $ω^2$.
The IKEA ASM Dataset: Understanding People Assembling Furniture through Actions, Objects and Pose
Venue: arXiv cs.CV 2023
Year: 2023

The availability of a large labeled dataset is a key requirement for applying deep learning methods to solve various computer vision tasks. In the context of understanding human activities, existing public datasets, while large in size, are often limited to a single RGB camera and provide only per-frame or per-clip action annotations. To enable richer analysis and understanding of human activities, we introduce IKEA ASM -- a three million frame, multi-view, furniture assembly video dataset that includes depth, atomic actions, object segmentation, and human pose. Additionally, we benchmark prominent methods for video action recognition, object segmentation and human pose estimation tasks on this challenging dataset. The dataset enables the development of holistic methods, which integrate multi-modal and multi-view data to better perform on these tasks.
Fractional Covers of Hypergraphs with Bounded Multi-Intersection
Venue: arXiv cs.DM 2023
Year: 2023

Fractional (hyper-)graph theory is concerned with the specific problems that arise when fractional analogues of otherwise integer-valued (hyper-)graph invariants are considered. The focus of this paper is on fractional edge covers of hypergraphs. Our main technical result generalizes and unifies previous conditions under which the size of the support of fractional edge covers is bounded independently of the size of the hypergraph itself. This allows us to extend previous tractability results for checking if the fractional hypertree width of a given hypergraph is $\leq k$ for some constant $k$. We also show how our results translate to fractional vertex covers.
Describing quantum metrology with erasure errors using weight distributions of classical codes
Venue: arXiv cs.IT 2023
Year: 2023

Quantum sensors are expected to be a prominent use-case of quantum technologies, but in practice, noise easily degrades their performance. Quantum sensors can for instance be afflicted with erasure errors. Here, we consider using quantum probe states with a structure that corresponds to classical $[n,k,d]$ binary block codes of minimum distance $d \geq t+1$. We obtain bounds on the ultimate precision that these probe states can give for estimating the unknown magnitude of a classical field after at most $t$ qubits of the quantum probe state are erased. We show that the quantum Fisher information is proportional to the variances of the weight distributions of the corresponding $2^t$ shortened codes. If the shortened codes of a fixed code with $d \geq t+1$ have a non-trivial weight distribution, then the probe states obtained by concatenating this code with repetition codes of increasing length enable asymptotically optimal field-sensing that passively tolerates up to $t$ erasure errors.
Improved Paths to Stability for the Stable Marriage Problem
Venue: arXiv cs.GT 2023
Year: 2023

The stable marriage problem requires one to find a marriage with no blocking pair. Given a matching that is not stable, Roth and Vande Vate have shown that there exists a sequence of matchings that leads to a stable matching in which each successive matching is obtained by satisfying a blocking pair. The sequence produced by Roth and Vande Vate's algorithm is of length $O(n^3)$ where $n$ is the number of men (and women). In this paper, we present an algorithm that achieves stability in a sequence of matchings of length $O(n^2)$. We also give an efficient algorithm to find the stable matching closest to the given initial matching under an appropriate distance function between matchings.
Incremental Without Replacement Sampling in Nonconvex Optimization
Venue: arXiv cs.LG 2023
Year: 2023

Minibatch decomposition methods for empirical risk minimization are commonly analysed in a stochastic approximation setting, also known as sampling with replacement. On the other hands modern implementations of such techniques are incremental: they rely on sampling without replacement, for which available analysis are much scarcer. We provide convergence guaranties for the latter variant by analysing a versatile incremental gradient scheme. For this scheme, we consider constant, decreasing or adaptive step sizes. In the smooth setting we obtain explicit complexity estimates in terms of epoch counter. In the nonsmooth setting we prove that the sequence is attracted by solutions of optimality conditions of the problem.
timeXplain -- A Framework for Explaining the Predictions of Time Series Classifiers
Venue: arXiv cs.LG 2023
Year: 2023

Modern time series classifiers display impressive predictive capabilities, yet their decision-making processes mostly remain black boxes to the user. At the same time, model-agnostic explainers, such as the recently proposed SHAP, promise to make the predictions of machine learning models interpretable, provided there are well-designed domain mappings. We bring both worlds together in our timeXplain framework, extending the reach of explainable artificial intelligence to time series classification and value prediction. We present novel domain mappings for the time domain, frequency domain, and time series statistics and analyze their explicative power as well as their limits. We employ a novel evaluation metric to experimentally compare timeXplain to several model-specific explanation approaches for state-of-the-art time series classifiers.