Given a set of changing entities, which ones are the most uptrending over some time T? Which entities are standing out as the biggest movers? To answer this question we define the concept of momentum. Two parameters - absolute gain and relative gain over time T play the key role in defining momentum. Neither alone is sufficient since they are each biased towards a subset of entities. Absolute gain favors large entities, while relative gain favors small ones. To accommodate both absolute and relative gain in an unbiased way, we define Pareto ordering between entities. For entity E to dominate another entity F in Pareto ordering, E's absolute and relative gains over time T must be higher than F's absolute and relative gains respectively. Momentum leaders are defined as maximal elements of this partial order - the Pareto frontier. We show how to compute momentum leaders and propose linear ordering among them to help rank entities with the most momentum on the top. Additionally, we show that when vectors follow power-law, the cardinality of the set of Momentum leaders (Pareto frontier) is of the order of square root of the logarithm of the number of entities, thus it is very small.
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There have recently been significant advances in the accuracy of algorithms proposed for time series classification (TSC). However, a commonly asked question by real world practitioners and data scientists less familiar with the research topic, is whether the complexity of the algorithms considered state of the art is really necessary. Many times the first approach suggested is a simple pipeline of summary statistics or other time series feature extraction approaches such as TSFresh, which in itself is a sensible question; in publications on TSC algorithms generalised for multiple problem types, we rarely see these approaches considered or compared against. We experiment with basic feature extractors using vector based classifiers shown to be effective with continuous attributes in current state-of-the-art time series classifiers. We test these approaches on the UCR time series dataset archive, looking to see if TSC literature has overlooked the effectiveness of these approaches. We find that a pipeline of TSFresh followed by a rotation forest classifier, which we name FreshPRINCE, performs best. It is not state of the art, but it is significantly more accurate than nearest neighbour with dynamic time warping, and represents a reasonable benchmark for future comparison.
Pair-wise loss is an approach to metric learning that learns a semantic embedding by optimizing a loss function that encourages images from the same semantic class to be mapped closer than images from different classes. The literature reports a large and growing set of variations of the pair-wise loss strategies. Here we decompose the gradient of these loss functions into components that relate to how they push the relative feature positions of the anchor-positive and anchor-negative pairs. This decomposition allows the unification of a large collection of current pair-wise loss functions. Additionally, explicitly constructing pair-wise gradient updates to separate out these effects gives insights into which have the biggest impact, and leads to a simple algorithm that beats the state of the art for image retrieval on the CAR, CUB and Stanford Online products datasets.
The angular measure on the unit sphere characterizes the first-order dependence structure of the components of a random vector in extreme regions and is defined in terms of standardized margins. Its statistical recovery is an important step in learning problems involving observations far away from the center. In the common situation that the components of the vector have different distributions, the rank transformation offers a convenient and robust way of standardizing data in order to build an empirical version of the angular measure based on the most extreme observations. However, the study of the sampling distribution of the resulting empirical angular measure is challenging. It is the purpose of the paper to establish finite-sample bounds for the maximal deviations between the empirical and true angular measures, uniformly over classes of Borel sets of controlled combinatorial complexity. The bounds are valid with high probability and, up to logarithmic factors, scale as the square root of the effective sample size. The bounds are applied to provide performance guarantees for two statistical learning procedures tailored to extreme regions of the input space and built upon the empirical angular measure: binary classification in extreme regions through empirical risk minimization and unsupervised anomaly detection through minimum-volume sets of the sphere.
We study the problem of efficiently computing on encoded data. More specifically, we study the question of low-bandwidth computation of functions $F:\mathbb{F}^k \to \mathbb{F}$ of some data $x \in \mathbb{F}^k$, given access to an encoding $c \in \mathbb{F}^n$ of $x$ under an error correcting code. In our model -- relevant in distributed storage, distributed computation and secret sharing -- each symbol of $c$ is held by a different party, and we aim to minimize the total amount of information downloaded from each party in order to compute $F(x)$. Special cases of this problem have arisen in several domains, and we believe that it is fruitful to study this problem in generality. Our main result is a low-bandwidth scheme to compute linear functions for Reed-Solomon codes, even in the presence of erasures. More precisely, let $\epsilon > 0$ and let $\mathcal{C}: \mathbb{F}^k \to \mathbb{F}^n$ be a full-length Reed-Solomon code of rate $1 - \epsilon$ over a field $\mathbb{F}$ with constant characteristic. For any $\gamma \in [0, \epsilon)$, our scheme can compute any linear function $F(x)$ given access to any $(1 - \gamma)$-fraction of the symbols of $\mathcal{C}(x)$, with download bandwidth $O(n/(\epsilon - \gamma))$ bits. In contrast, the naive scheme that involves reconstructing the data $x$ and then computing $F(x)$ uses $\Theta(n \log n)$ bits. Our scheme has applications in distributed storage, coded computation, and homomorphic secret sharing.
We consider the problem of discovering $K$ related Gaussian directed acyclic graphs (DAGs), where the involved graph structures share a consistent causal order and sparse unions of supports. Under the multi-task learning setting, we propose a $l_1/l_2$-regularized maximum likelihood estimator (MLE) for learning $K$ linear structural equation models. We theoretically show that the joint estimator, by leveraging data across related tasks, can achieve a better sample complexity for recovering the causal order (or topological order) than separate estimations. Moreover, the joint estimator is able to recover non-identifiable DAGs, by estimating them together with some identifiable DAGs. Lastly, our analysis also shows the consistency of union support recovery of the structures. To allow practical implementation, we design a continuous optimization problem whose optimizer is the same as the joint estimator and can be approximated efficiently by an iterative algorithm. We validate the theoretical analysis and the effectiveness of the joint estimator in experiments.
Reward is the driving force for reinforcement-learning agents. This paper is dedicated to understanding the expressivity of reward as a way to capture tasks that we would want an agent to perform. We frame this study around three new abstract notions of "task" that might be desirable: (1) a set of acceptable behaviors, (2) a partial ordering over behaviors, or (3) a partial ordering over trajectories. Our main results prove that while reward can express many of these tasks, there exist instances of each task type that no Markov reward function can capture. We then provide a set of polynomial-time algorithms that construct a Markov reward function that allows an agent to optimize tasks of each of these three types, and correctly determine when no such reward function exists. We conclude with an empirical study that corroborates and illustrates our theoretical findings.
Pre-trained Language Models (PLMs) have shown superior performance on various downstream Natural Language Processing (NLP) tasks. However, conventional pre-training objectives do not explicitly model relational facts in text, which are crucial for textual understanding. To address this issue, we propose a novel contrastive learning framework ERICA to obtain a deep understanding of the entities and their relations in text. Specifically, we define two novel pre-training tasks to better understand entities and relations: (1) the entity discrimination task to distinguish which tail entity can be inferred by the given head entity and relation; (2) the relation discrimination task to distinguish whether two relations are close or not semantically, which involves complex relational reasoning. Experimental results demonstrate that ERICA can improve typical PLMs (BERT and RoBERTa) on several language understanding tasks, including relation extraction, entity typing and question answering, especially under low-resource settings.
Named entity recognition (NER) and entity linking (EL) are two fundamentally related tasks, since in order to perform EL, first the mentions to entities have to be detected. However, most entity linking approaches disregard the mention detection part, assuming that the correct mentions have been previously detected. In this paper, we perform joint learning of NER and EL to leverage their relatedness and obtain a more robust and generalisable system. For that, we introduce a model inspired by the Stack-LSTM approach (Dyer et al., 2015). We observe that, in fact, doing multi-task learning of NER and EL improves the performance in both tasks when comparing with models trained with individual objectives. Furthermore, we achieve results competitive with the state-of-the-art in both NER and EL.
Data augmentation is rapidly gaining attention in machine learning. Synthetic data can be generated by simple transformations or through the data distribution. In the latter case, the main challenge is to estimate the label associated to new synthetic patterns. This paper studies the effect of generating synthetic data by convex combination of patterns and the use of these as unsupervised information in a semi-supervised learning framework with support vector machines, avoiding thus the need to label synthetic examples. We perform experiments on a total of 53 binary classification datasets. Our results show that this type of data over-sampling supports the well-known cluster assumption in semi-supervised learning, showing outstanding results for small high-dimensional datasets and imbalanced learning problems.
In order to answer natural language questions over knowledge graphs, most processing pipelines involve entity and relation linking. Traditionally, entity linking and relation linking has been performed either as dependent sequential tasks or independent parallel tasks. In this paper, we propose a framework called "EARL", which performs entity linking and relation linking as a joint single task. EARL uses a graph connection based solution to the problem. We model the linking task as an instance of the Generalised Travelling Salesman Problem (GTSP) and use GTSP approximate algorithm solutions. We later develop EARL which uses a pair-wise graph-distance based solution to the problem.The system determines the best semantic connection between all keywords of the question by referring to a knowledge graph. This is achieved by exploiting the "connection density" between entity candidates and relation candidates. The "connection density" based solution performs at par with the approximate GTSP solution.We have empirically evaluated the framework on a dataset with 5000 questions. Our system surpasses state-of-the-art scores for entity linking task by reporting an accuracy of 0.65 to 0.40 from the next best entity linker.
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