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 Statistical Learning


NeurIPS 2021

#artificialintelligence

The Machine Learning Meets Econometrics (MLECON) workshop will serve as an interface for researchers from machine learning and econometrics to understand challenges and recognize opportunities that arise from the synergy between these two disciplines as well as to exchange new ideas that will help propel the fields. Our one-day workshop will consist of invited talks from world-renowned experts, shorter talks from contributed authors, a Gather.Town poster session, and an interdisciplinary panel discussion. To encourage cross-over discussion among those publishing in different venues, the topic of our panel discussion will be "Machine Learning in Social Systems: Challenges and Opportunities from Program Evaluation". It was designed to highlight the complexity of evaluating social and economic programs as well as shortcomings of current approaches in machine learning and opportunities for methodological innovation. These challenges include more complex environments (markets, equilibrium, temporal considerations) and behavior (heterogeneity, delayed effects, unobserved confounders, strategic response). Our team of organizers and program committees is diverse in terms of gender, race, affiliations, country of origin, disciplinary background, and seniority levels. We aim to convene a broad variety of viewpoints on methodological axes (nonparametrics, machine learning, econometrics) as well as areas of application.


The Maths Behind Linear Regression

#artificialintelligence

Let us discuss Linear Regression, a type of Supervised Learning algorithm often used in Data Science and other ML related predictive models, and the maths behind it. Feature data values are also called independent variables because they are not influenced by anything, they are just the property of that particular dataset. Similarly target data values are also called dependent variables because they are in some way related to the feature or dependent variables. We know that our data will not all be related in the same linear manner. Based on this, our task in Linear Regression is to find the best possible relationship for which the error or deviation of the actual target from the target that we get from our relationship is as small as possible.


Two minutes NLP -- Doc2Vec in a nutshell

#artificialintelligence

Doc2Vec is an unsupervised algorithm that learns embeddings from variable-length pieces of texts, such as sentences, paragraphs, and documents. It's originally presented in the paper Distributed Representations of Sentences and Documents. Let's review Word2Vec first, as it provides the inspiration for the Doc2Vec algorithm. Word2Vec learns word vectors by predicting a word in a sentence using the other words in the context. In this framework, every word is mapped to a unique vector, represented by a column in a matrix W. The concatenation or sum of the vectors is then used as features for the prediction of the next word in a sentence. The word vectors are trained using stochastic gradient descent.


ELF: Exact-Lipschitz Based Universal Density Approximator Flow

arXiv.org Machine Learning

Normalizing flows have become more popular within the last few years; however, they continue to have limitations compared to other generative models, more specifically that they are computationally expensive in terms of memory and time. Early implementations of Normalizing Flows were coupling layers (Dinh et al., 2014, 2017; Kingma and Dhariwal, 2018) and autoregressive flows (Papamakarios et al., 2017; Kingma et al., 2016). These have easy to compute log-likelihoods; however, coupling layers tend to need quite a few parameters to achieve strong performance and autoregressive flows are extremely expensive to sample from. The newer technique of residual flows (Chen et al., 2019) allows for models that are built on standard components and have inductive biases that favor simpler functions (Gopal, 2020); however, these have the problem of being expensive in terms of time for computing log-likelihoods and training, as well as require quite a few layers for strong performance. Since the introduction of these models, there have been many developments that have lead to improvement in parameter efficiency such as FFJORD (Grathwohl et al., 2019), a continuous normalizing flow, that has a dynamic number of layers. However, this too can have computational problems as having a few dynamics layers can lead to hundreds of implicit layers. Among the flows introduced, the ones with provable universal approximation capability are Affine Coupling Layers (Dinh et al., 2014, 2017; Teshima et al., 2020), Neural Autoregressive Flows (NAF, Huang et al. (2018)), Block NAFs (BNAF, Cao et al. (2019)), Sum-of-Squares Polynomial Flow (Jaini et al., 2019), and Convex Potential Flows (CP-Flow, Huang et al. (2021)). Though these have been shown to be universal approximators, they do not necessarily translate into faster, more efficient training, and some of the flows listed require the expensive sampling routine of autoregressive flows.


Progressive Graph Convolution Network for EEG Emotion Recognition

arXiv.org Artificial Intelligence

Studies in the area of neuroscience have revealed the relationship between emotional patterns and brain functional regions, demonstrating that dynamic relationships between different brain regions are an essential factor affecting emotion recognition determined through electroencephalography (EEG). Moreover, in EEG emotion recognition, we can observe that clearer boundaries exist between coarse-grained emotions than those between fine-grained emotions, based on the same EEG data; this indicates the concurrence of large coarse- and small fine-grained emotion variations. Thus, the progressive classification process from coarse- to fine-grained categories may be helpful for EEG emotion recognition. Consequently, in this study, we propose a progressive graph convolution network (PGCN) for capturing this inherent characteristic in EEG emotional signals and progressively learning the discriminative EEG features. To fit different EEG patterns, we constructed a dual-graph module to characterize the intrinsic relationship between different EEG channels, containing the dynamic functional connections and static spatial proximity information of brain regions from neuroscience research. Moreover, motivated by the observation of the relationship between coarse- and fine-grained emotions, we adopt a dual-head module that enables the PGCN to progressively learn more discriminative EEG features, from coarse-grained (easy) to fine-grained categories (difficult), referring to the hierarchical characteristic of emotion. To verify the performance of our model, extensive experiments were conducted on two public datasets: SEED-IV and multi-modal physiological emotion database (MPED).


Translating Human Mobility Forecasting through Natural Language Generation

arXiv.org Artificial Intelligence

Existing human mobility forecasting models follow the standard design of the time-series prediction model which takes a series of numerical values as input to generate a numerical value as a prediction. Although treating this as a regression problem seems straightforward, incorporating various contextual information such as the semantic category information of each Place-of-Interest (POI) is a necessary step, and often the bottleneck, in designing an effective mobility prediction model. As opposed to the typical approach, we treat forecasting as a translation problem and propose a novel forecasting through a language generation pipeline. The paper aims to address the human mobility forecasting problem as a language translation task in a sequence-to-sequence manner. A mobility-to-language template is first introduced to describe the numerical mobility data as natural language sentences. The core intuition of the human mobility forecasting translation task is to convert the input mobility description sentences into a future mobility description from which the prediction target can be obtained. Under this pipeline, a two-branch network, SHIFT (Translating Human Mobility Forecasting), is designed. Specifically, it consists of one main branch for language generation and one auxiliary branch to directly learn mobility patterns. During the training, we develop a momentum mode for better connecting and training the two branches. Extensive experiments on three real-world datasets demonstrate that the proposed SHIFT is effective and presents a new revolutionary approach to forecasting human mobility.


Ex-Model: Continual Learning from a Stream of Trained Models

arXiv.org Artificial Intelligence

Learning continually from non-stationary data streams is a challenging research topic of growing popularity in the last few years. Being able to learn, adapt, and generalize continually in an efficient, effective, and scalable way is fundamental for a sustainable development of Artificial Intelligent systems. However, an agent-centric view of continual learning requires learning directly from raw data, which limits the interaction between independent agents, the efficiency, and the privacy of current approaches. Instead, we argue that continual learning systems should exploit the availability of compressed information in the form of trained models. In this paper, we introduce and formalize a new paradigm named "Ex-Model Continual Learning" (ExML), where an agent learns from a sequence of previously trained models instead of raw data. We further contribute with three ex-model continual learning algorithms and an empirical setting comprising three datasets (MNIST, CIFAR-10 and CORe50), and eight scenarios, where the proposed algorithms are extensively tested. Finally, we highlight the peculiarities of the ex-model paradigm and we point out interesting future research directions.


Linear Discriminant Analysis with High-dimensional Mixed Variables

arXiv.org Machine Learning

Datasets containing both categorical and continuous variables are frequently encountered in many areas, and with the rapid development of modern measurement technologies, the dimensions of these variables can be very high. Despite the recent progress made in modelling high-dimensional data for continuous variables, there is a scarcity of methods that can deal with a mixed set of variables. To fill this gap, this paper develops a novel approach for classifying high-dimensional observations with mixed variables. Our framework builds on a location model, in which the distributions of the continuous variables conditional on categorical ones are assumed Gaussian. We overcome the challenge of having to split data into exponentially many cells, or combinations of the categorical variables, by kernel smoothing, and provide new perspectives for its bandwidth choice to ensure an analogue of Bochner's Lemma, which is different to the usual bias-variance tradeoff. We show that the two sets of parameters in our model can be separately estimated and provide penalized likelihood for their estimation. Results on the estimation accuracy and the misclassification rates are established, and the competitive performance of the proposed classifier is illustrated by extensive simulation and real data studies.


How to Learn when Data Gradually Reacts to Your Model

arXiv.org Machine Learning

A recent line of work has focused on training machine learning (ML) models in the performative setting, i.e. when the data distribution reacts to the deployed model. The goal in this setting is to learn a model which both induces a favorable data distribution and performs well on the induced distribution, thereby minimizing the test loss. Previous work on finding an optimal model assumes that the data distribution immediately adapts to the deployed model. In practice, however, this may not be the case, as the population may take time to adapt to the model. In many applications, the data distribution depends on both the currently deployed ML model and on the "state" that the population was in before the model was deployed. In this work, we propose a new algorithm, Stateful Performative Gradient Descent (Stateful PerfGD), for minimizing the performative loss even in the presence of these effects. We provide theoretical guarantees for the convergence of Stateful PerfGD. Our experiments confirm that Stateful PerfGD substantially outperforms previous state-of-the-art methods.


Addressing Bias in Active Learning with Depth Uncertainty Networks... or Not

arXiv.org Machine Learning

Farquhar et al. [2021] show that correcting for active learning bias with underparameterised models leads to improved downstream performance. For overparameterised models such as NNs, however, correction leads either to decreased or unchanged performance. They suggest that this is due to an "overfitting bias" which offsets the active learning bias. We show that depth uncertainty networks operate in a low overfitting regime, much like underparameterised models. They should therefore see an increase in performance with bias correction. Surprisingly, they do not. We propose that this negative result, as well as the results Farquhar et al. [2021], can be explained via the lens of the bias-variance decomposition of generalisation error.