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 Statistical Learning


The implicit fairness criterion of unconstrained learning

arXiv.org Machine Learning

We clarify what fairness guarantees we can and cannot expect to follow from unconstrained machine learning. Specifically, we characterize when unconstrained learning on its own implies group calibration, that is, the outcome variable is conditionally independent of group membership given the score. We show that under reasonable conditions, the deviation from satisfying group calibration is upper bounded by the excess risk of the learned score relative to the Bayes optimal score function. A lower bound confirms the optimality of our upper bound. Moreover, we prove that as the excess risk of the learned score decreases, it strongly violates separation and independence, two other standard fairness criteria. Our results show that group calibration is the fairness criterion that unconstrained learning implicitly favors. On the one hand, this means that calibration is often satisfied on its own without the need for active intervention, albeit at the cost of violating other criteria that are at odds with calibration. On the other hand, it suggests that we should be satisfied with calibration as a fairness criterion only if we are at ease with the use of unconstrained machine learning in a given application.


Positive and Unlabeled Learning through Negative Selection and Imbalance-aware Classification

arXiv.org Machine Learning

Motivated by applications in protein function prediction, we consider a challenging supervised classification setting in which positive labels are scarce and there are no explicit negative labels. The learning algorithm must thus select which unlabeled examples to use as negative training points, possibly ending up with an unbalanced learning problem. We address these issues by proposing an algorithm that combines active learning (for selecting negative examples) with imbalance-aware learning (for mitigating the label imbalance). In our experiments we observe that these two techniques operate synergistically, outperforming state-of-the-art methods on standard protein function prediction benchmarks.


Stopping Active Learning based on Predicted Change of F Measure for Text Classification

arXiv.org Machine Learning

Abstract--During active learning, an effective stopping method allows users to limit the number of annotations, which is cost effective. In this paper, a new stopping method called Predicted Change of F Measure will be introduced that attempts to provide the users an estimate of how much performance of the model is changing at each iteration. This stopping method can be applied with any base learner. This method is useful for reducing the data annotation bottleneck encountered when building text classification systems. I. INTRODUCTION The use of active learning to train machine learning models has been used as a way to reduce annotation costs for text and speech processing applications [1], [2], [3], [4], [5]. Active learning has been shown to have a particularly large potential for reducing annotation cost for text classification [6], [7]. Text classification is one of the most important fields in semantic computing and it has been used in many applications [8], [9], [10], [11], [12]. A. Active Learning Active learning is a form of machine learning that gives the model the ability to select the data on which it wants to learn from and to choose when to end the process of training. In active learning, the model is first provided a small batch of annotated data to be trained on. Then, in each following iteration, the model selects a small batch and removes this batch from a large unlabeled set of examples.


Learning Models from Data with Measurement Error: Tackling Underreporting

arXiv.org Machine Learning

Measurement error in observational datasets can lead to systematic bias in inferences based on these datasets. As studies based on observational data are increasingly used to inform decisions with real-world impact, it is critical that we develop a robust set of techniques for analyzing and adjusting for these biases. In this paper we present a method for estimating the distribution of an outcome given a binary exposure that is subject to underreporting. Our method is based on a missing data view of the measurement error problem, where the true exposure is treated as a latent variable that is marginalized out of a joint model. We prove three different conditions under which the outcome distribution can still be identified from data containing only error-prone observations of the exposure. We demonstrate this method on synthetic data and analyze its sensitivity to near violations of the identifiability conditions. Finally, we use this method to estimate the effects of maternal smoking and opioid use during pregnancy on childhood obesity, two import problems from public health. Using the proposed method, we estimate these effects using only subject-reported drug use data and substantially refine the range of estimates generated by a sensitivity analysis-based approach. Further, the estimates produced by our method are consistent with existing literature on both the effects of maternal smoking and the rate at which subjects underreport smoking.


Unified estimation framework for unnormalized models with statistical efficiency

arXiv.org Machine Learning

Parameter estimation of unnormalized models is a challenging problem because normalizing constants are not calculated explicitly and maximum likelihood estimation is computationally infeasible. Although some consistent estimators have been proposed earlier, the problem of statistical efficiency does remain. In this study, we propose a unified, statistically efficient estimation framework for unnormalized models and several novel efficient estimators with reasonable computational time regardless of whether the sample space is discrete or continuous. The loss functions of the proposed estimators are derived by combining the following two methods: (1) density-ratio matching using Bregman divergence, and (2) plugging-in nonparametric estimators. We also analyze the properties of the proposed estimators when the unnormalized model is misspecified. Finally, the experimental results demonstrate the advantages of our method over existing approaches.


Novel Results Considered Harmful

#artificialintelligence

Ravi Adve from University of Toronto graciously invited me to give a public lecture at the university earlier this summer. I was very grateful for the opportunity. The university's facilities were fantastic, and Ravi did a wonderful job organizing everything. The audience was engaging and asked thoughtful questions, and the attendance was much higher than I had anticipated for a Tuesday morning lecture in the middle of summer! There was great representation from multiple departments, including Electrical and Computer Engineering, Computer Science, and Mathematics.


Learning to compress and search visual data in large-scale systems

arXiv.org Machine Learning

The problem of high-dimensional and large-scale representation of visual data is addressed from an unsupervised learning perspective. The emphasis is put on discrete representations, where the description length can be measured in bits and hence the model capacity can be controlled. The algorithmic infrastructure is developed based on the synthesis and analysis prior models whose rate-distortion properties, as well as capacity vs. sample complexity trade-offs are carefully optimized. These models are then extended to multi-layers, namely the RRQ and the ML-STC frameworks, where the latter is further evolved as a powerful deep neural network architecture with fast and sample-efficient training and discrete representations. For the developed algorithms, three important applications are developed. First, the problem of large-scale similarity search in retrieval systems is addressed, where a double-stage solution is proposed leading to faster query times and shorter database storage. Second, the problem of learned image compression is targeted, where the proposed models can capture more redundancies from the training images than the conventional compression codecs. Finally, the proposed algorithms are used to solve ill-posed inverse problems. In particular, the problems of image denoising and compressive sensing are addressed with promising results.


Learning Vector Representation of Content and Matrix Representation of Change: Towards a Representational Model of V1

arXiv.org Machine Learning

This paper entertains the hypothesis that the primary purpose of the cells of the primary visual cortex (V1) is to perceive motions and predict changes of local image contents. Specifically, we propose a model that couples the vector representations of local image contents with the matrix representations of local pixel displacements caused by the relative motions between the agent and the surrounding objects and scene. When the image changes from one time frame to the next due to pixel displacements, the vector at each pixel is multiplied by a matrix that represents the displacement of this pixel. We show that by learning from pair of images that are deformed versions of each other, we can learn both vector and matrix representations. The units in the learned vector representations resemble V1 cells. The learned vector-matrix representations enable prediction of image frames over time, and more importantly, inference of the local pixel displacements caused by relative motions.


Orthogonal Statistical Learning

arXiv.org Machine Learning

We provide excess risk guarantees for statistical learning in the presence of an unknown nuisance component. We analyze a two-stage sample splitting meta-algorithm that takes as input two arbitrary estimation algorithms: one for the target model and one for the nuisance model. We show that if the population risk satisfies a condition called Neyman orthogonality, the impact of the first stage error on the excess risk bound achieved by the meta-algorithm is of second order. Our general theorem is agnostic to the particular algorithms used for the target and nuisance and only makes an assumption on their individual performance. This enables the use of a plethora of existing results from statistical learning and machine learning literature to give new guarantees for learning with a nuisance component. Moreover, by focusing on excess risk rather than parameter estimation, we can give guarantees under weaker assumptions than in previous works and accommodate the case where the target parameter belongs to a complex nonparametric class. When the nuisance and target parameters belong to arbitrary classes, we characterize conditions on the metric entropy such that oracle rates---rates of the same order as if we knew the nuisance model---are achieved. We also analyze the rates achieved by specific estimation algorithms such as variance-penalized empirical risk minimization, neural network estimation and sparse high-dimensional linear model estimation. We highlight the applicability of our results via four applications of primary importance: 1) heterogeneous treatment effect estimation, 2) offline policy optimization, 3) domain adaptation, and 4) learning with missing data.


A Zero-Shot Learning application in Deep Drawing process using Hyper-Process Model

arXiv.org Machine Learning

One of the consequences of passing from mass production to mass customization paradigm in the nowadays industrialized world is the need to increase flexibility and responsiveness of manufacturing companies. The high-mix / low-volume production forces constant accommodations of unknown product variants, which ultimately leads to high periods of machine calibration. The difficulty related with machine calibration is that experience is required together with a set of experiments to meet the final product quality. Unfortunately, all possible combinations of machine parameters is so high that is difficult to build empirical knowledge. Due to this fact, normally trial and error approaches are taken making one-of-a-kind products not viable. Therefore, a Zero-Shot Learning (ZSL) based approach called hyper-process model (HPM) to learn the relation among multiple tasks is used as a way to shorten the calibration phase. Assuming each product variant is a task to solve, first, a shape analysis on data to learn common modes of deformation between tasks is made, and secondly, a mapping between these modes and task descriptions is performed. Ultimately, the present work has two main contributions: 1) Formulation of an industrial problem into a ZSL setting where new process models can be generated for process optimization and 2) the definition of a regression problem in the domain of ZSL. For that purpose, a 2-d deep drawing simulated process was used based on data collected from the Abaqus simulator, where a significant number of process models were collected to test the effectiveness of the approach. The obtained results show that is possible to learn new tasks without any available data (both labeled and unlabeled) by leveraging information about already existing tasks, allowing to speed up the calibration phase and make a quicker integration of new products into manufacturing systems.