We study the problem of constructing coresets for clustering problems with time series data. This problem has gained importance across many fields including biology, medicine, and economics due to the proliferation of sensors facilitating real-time measurement and rapid drop in storage costs. In particular, we consider the setting where the time series data on $N$ entities is generated from a Gaussian mixture model with autocorrelations over $k$ clusters in $\mathbb{R}^d$. Our main contribution is an algorithm to construct coresets for the maximum likelihood objective for this mixture model. Our algorithm is efficient, and under a mild boundedness assumption on the covariance matrices of the underlying Gaussians, the size of the coreset is independent of the number of entities $N$ and the number of observations for each entity, and depends only polynomially on $k$, $d$ and $1/\varepsilon$, where $\varepsilon$ is the error parameter. We empirically assess the performance of our coreset with synthetic data.
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We derive general, yet simple, sharp bounds on the size of the omitted variable bias for a broad class of causal parameters that can be identified as linear functionals of the conditional expectation function of the outcome. Such functionals encompass many of the traditional targets of investigation in causal inference studies, such as, for example, (weighted) average of potential outcomes, average treatment effects (including subgroup effects, such as the effect on the treated), (weighted) average derivatives, and policy effects from shifts in covariate distribution -- all for general, nonparametric causal models. Our construction relies on the Riesz-Frechet representation of the target functional. Specifically, we show how the bound on the bias depends only on the additional variation that the latent variables create both in the outcome and in the Riesz representer for the parameter of interest. Moreover, in many important cases (e.g, average treatment effects in partially linear models, or in nonseparable models with a binary treatment) the bound is shown to depend on two easily interpretable quantities: the nonparametric partial $R^2$ (Pearson's "correlation ratio") of the unobserved variables with the treatment and with the outcome. Therefore, simple plausibility judgments on the maximum explanatory power of omitted variables (in explaining treatment and outcome variation) are sufficient to place overall bounds on the size of the bias. Finally, leveraging debiased machine learning, we provide flexible and efficient statistical inference methods to estimate the components of the bounds that are identifiable from the observed distribution.
The class imbalance problem, as an important issue in learning node representations, has drawn increasing attention from the community. Although the imbalance considered by existing studies roots from the unequal quantity of labeled examples in different classes (quantity imbalance), we argue that graph data expose a unique source of imbalance from the asymmetric topological properties of the labeled nodes, i.e., labeled nodes are not equal in terms of their structural role in the graph (topology imbalance). In this work, we first probe the previously unknown topology-imbalance issue, including its characteristics, causes, and threats to semi-supervised node classification learning. We then provide a unified view to jointly analyzing the quantity- and topology- imbalance issues by considering the node influence shift phenomenon with the Label Propagation algorithm. In light of our analysis, we devise an influence conflict detection -- based metric Totoro to measure the degree of graph topology imbalance and propose a model-agnostic method ReNode to address the topology-imbalance issue by re-weighting the influence of labeled nodes adaptively based on their relative positions to class boundaries. Systematic experiments demonstrate the effectiveness and generalizability of our method in relieving topology-imbalance issue and promoting semi-supervised node classification. The further analysis unveils varied sensitivity of different graph neural networks (GNNs) to topology imbalance, which may serve as a new perspective in evaluating GNN architectures.
The focus of disentanglement approaches has been on identifying independent factors of variation in data. However, the causal variables underlying real-world observations are often not statistically independent. In this work, we bridge the gap to real-world scenarios by analyzing the behavior of the most prominent disentanglement approaches on correlated data in a large-scale empirical study (including 4260 models). We show and quantify that systematically induced correlations in the dataset are being learned and reflected in the latent representations, which has implications for downstream applications of disentanglement such as fairness. We also demonstrate how to resolve these latent correlations, either using weak supervision during training or by post-hoc correcting a pre-trained model with a small number of labels.
Unsupervised (or self-supervised) graph representation learning is essential to facilitate various graph data mining tasks when external supervision is unavailable. The challenge is to encode the information about the graph structure and the attributes associated with the nodes and edges into a low dimensional space. Most existing unsupervised methods promote similar representations across nodes that are topologically close. Recently, it was shown that leveraging additional graph-level information, e.g., information that is shared among all nodes, encourages the representations to be mindful of the global properties of the graph, which greatly improves their quality. However, in most graphs, there is significantly more structure that can be captured, e.g., nodes tend to belong to (multiple) clusters that represent structurally similar nodes. Motivated by this observation, we propose a graph representation learning method called Graph InfoClust (GIC), that seeks to additionally capture cluster-level information content. These clusters are computed by a differentiable K-means method and are jointly optimized by maximizing the mutual information between nodes of the same clusters. This optimization leads the node representations to capture richer information and nodal interactions, which improves their quality. Experiments show that GIC outperforms state-of-art methods in various downstream tasks (node classification, link prediction, and node clustering) with a 0.9% to 6.1% gain over the best competing approach, on average.
Combining clustering and representation learning is one of the most promising approaches for unsupervised learning of deep neural networks. However, doing so naively leads to ill posed learning problems with degenerate solutions. In this paper, we propose a novel and principled learning formulation that addresses these issues. The method is obtained by maximizing the information between labels and input data indices. We show that this criterion extends standard cross-entropy minimization to an optimal transport problem, which we solve efficiently for millions of input images and thousands of labels using a fast variant of the Sinkhorn-Knopp algorithm. The resulting method is able to self-label visual data so as to train highly competitive image representations without manual labels. Compared to the best previous method in this class, namely DeepCluster, our formulation minimizes a single objective function for both representation learning and clustering; it also significantly outperforms DeepCluster in standard benchmarks and reaches state of the art for learning a ResNet-50 self-supervisedly.
User behavior data in recommender systems are driven by the complex interactions of many latent factors behind the users' decision making processes. The factors are highly entangled, and may range from high-level ones that govern user intentions, to low-level ones that characterize a user's preference when executing an intention. Learning representations that uncover and disentangle these latent factors can bring enhanced robustness, interpretability, and controllability. However, learning such disentangled representations from user behavior is challenging, and remains largely neglected by the existing literature. In this paper, we present the MACRo-mIcro Disentangled Variational Auto-Encoder (MacridVAE) for learning disentangled representations from user behavior. Our approach achieves macro disentanglement by inferring the high-level concepts associated with user intentions (e.g., to buy a shirt or a cellphone), while capturing the preference of a user regarding the different concepts separately. A micro-disentanglement regularizer, stemming from an information-theoretic interpretation of VAEs, then forces each dimension of the representations to independently reflect an isolated low-level factor (e.g., the size or the color of a shirt). Empirical results show that our approach can achieve substantial improvement over the state-of-the-art baselines. We further demonstrate that the learned representations are interpretable and controllable, which can potentially lead to a new paradigm for recommendation where users are given fine-grained control over targeted aspects of the recommendation lists.
Pre-trained language representation models, such as BERT, capture a general language representation from large-scale corpora, but lack domain-specific knowledge. When reading a domain text, experts make inferences with relevant knowledge. For machines to achieve this capability, we propose a knowledge-enabled language representation model (K-BERT) with knowledge graphs (KGs), in which triples are injected into the sentences as domain knowledge. However, too much knowledge incorporation may divert the sentence from its correct meaning, which is called knowledge noise (KN) issue. To overcome KN, K-BERT introduces soft-position and visible matrix to limit the impact of knowledge. K-BERT can easily inject domain knowledge into the models by equipped with a KG without pre-training by-self because it is capable of loading model parameters from the pre-trained BERT. Our investigation reveals promising results in twelve NLP tasks. Especially in domain-specific tasks (including finance, law, and medicine), K-BERT significantly outperforms BERT, which demonstrates that K-BERT is an excellent choice for solving the knowledge-driven problems that require experts.
Question answering over knowledge graphs (KGQA) has evolved from simple single-fact questions to complex questions that require graph traversal and aggregation. We propose a novel approach for complex KGQA that uses unsupervised message passing, which propagates confidence scores obtained by parsing an input question and matching terms in the knowledge graph to a set of possible answers. First, we identify entity, relationship, and class names mentioned in a natural language question, and map these to their counterparts in the graph. Then, the confidence scores of these mappings propagate through the graph structure to locate the answer entities. Finally, these are aggregated depending on the identified question type. This approach can be efficiently implemented as a series of sparse matrix multiplications mimicking joins over small local subgraphs. Our evaluation results show that the proposed approach outperforms the state-of-the-art on the LC-QuAD benchmark. Moreover, we show that the performance of the approach depends only on the quality of the question interpretation results, i.e., given a correct relevance score distribution, our approach always produces a correct answer ranking. Our error analysis reveals correct answers missing from the benchmark dataset and inconsistencies in the DBpedia knowledge graph. Finally, we provide a comprehensive evaluation of the proposed approach accompanied with an ablation study and an error analysis, which showcase the pitfalls for each of the question answering components in more detail.
We present a new clustering method in the form of a single clustering equation that is able to directly discover groupings in the data. The main proposition is that the first neighbor of each sample is all one needs to discover large chains and finding the groups in the data. In contrast to most existing clustering algorithms our method does not require any hyper-parameters, distance thresholds and/or the need to specify the number of clusters. The proposed algorithm belongs to the family of hierarchical agglomerative methods. The technique has a very low computational overhead, is easily scalable and applicable to large practical problems. Evaluation on well known datasets from different domains ranging between 1077 and 8.1 million samples shows substantial performance gains when compared to the existing clustering techniques.
Kernel methods have produced state-of-the-art results for a number of NLP tasks such as relation extraction, but suffer from poor scalability due to the high cost of computing kernel similarities between discrete natural language structures. A recently proposed technique, kernelized locality-sensitive hashing (KLSH), can significantly reduce the computational cost, but is only applicable to classifiers operating on kNN graphs. Here we propose to use random subspaces of KLSH codes for efficiently constructing an explicit representation of NLP structures suitable for general classification methods. Further, we propose an approach for optimizing the KLSH model for classification problems by maximizing a variational lower bound on mutual information between the KLSH codes (feature vectors) and the class labels. We evaluate the proposed approach on biomedical relation extraction datasets, and observe significant and robust improvements in accuracy w.r.t. state-of-the-art classifiers, along with drastic (orders-of-magnitude) speedup compared to conventional kernel methods.
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