Christian Hansen

Christian Hansen, Casper Hansen, Stephen Alstrup et al.

Modelling sequential music skips provides streaming companies the ability to better understand the needs of the user base, resulting in a better user experience by reducing the need to manually skip certain music tracks. This paper describes the solution of the University of Copenhagen DIKU-IR team in the 'Spotify Sequential Skip Prediction Challenge', where the task was to predict the skip behaviour of the second half in a music listening session conditioned on the first half. We model this task using a Multi-RNN approach consisting of two distinct stacked recurrent neural networks, where one network focuses on encoding the first half of the session and the other network focuses on utilizing the encoding to make sequential skip predictions. The encoder network is initialized by a learned session-wide music encoding, and both of them utilize a learned track embedding. Our final model consists of a majority voted ensemble of individually trained models, and ranked 2nd out of 45 participating teams in the competition with a mean average accuracy of 0.641 and an accuracy on the first skip prediction of 0.807. Our code is released at https://github.com/Varyn/WSDM-challenge-2019-spotify.

Victor Chernozhukov, Christian Hansen, Nathan Kallus et al.

An introduction to the emerging fusion of machine learning and causal inference. The book presents ideas from classical structural equation models (SEMs) and their modern AI equivalent, directed acyclical graphs (DAGs) and structural causal models (SCMs), and covers Double/Debiased Machine Learning methods to do inference in such models using modern predictive tools.

Gino Gulamhussene, Anneke Meyer, Marko Rak et al.

Organ motion poses an unresolved challenge in image-guided interventions. In the pursuit of solving this problem, the research field of time-resolved volumetric magnetic resonance imaging (4D MRI) has evolved. However, current techniques are unsuitable for most interventional settings because they lack sufficient temporal and/or spatial resolution or have long acquisition times. In this work, we propose a novel approach for real-time, high-resolution 4D MRI with large fields of view for MR-guided interventions. To this end, we trained a convolutional neural network (CNN) end-to-end to predict a 3D liver MRI that correctly predicts the liver's respiratory state from a live 2D navigator MRI of a subject. Our method can be used in two ways: First, it can reconstruct near real-time 4D MRI with high quality and high resolution (209x128x128 matrix size with isotropic 1.8mm voxel size and 0.6s/volume) given a dynamic interventional 2D navigator slice for guidance during an intervention. Second, it can be used for retrospective 4D reconstruction with a temporal resolution of below 0.2s/volume for motion analysis and use in radiation therapy. We report a mean target registration error (TRE) of 1.19 $\pm$0.74mm, which is below voxel size. We compare our results with a state-of-the-art retrospective 4D MRI reconstruction. Visual evaluation shows comparable quality. We show that small training sizes with short acquisition times down to 2min can already achieve promising results and 24min are sufficient for high quality results. Because our method can be readily combined with earlier methods, acquisition time can be further decreased while also limiting quality loss. We show that an end-to-end, deep learning formulation is highly promising for 4D MRI reconstruction.

Christian Hansen

Sequential modelling entails making sense of sequential data, which naturally occurs in a wide array of domains. One example is systems that interact with users, log user actions and behaviour, and make recommendations of items of potential interest to users on the basis of their previous interactions. In such cases, the sequential order of user interactions is often indicative of what the user is interested in next. Similarly, for systems that automatically infer the semantics of text, capturing the sequential order of words in a sentence is essential, as even a slight re-ordering could significantly alter its original meaning. This thesis makes methodological contributions and new investigations of sequential modelling for the specific application areas of systems that recommend music tracks to listeners and systems that process text semantics in order to automatically fact-check claims, or "speed read" text for efficient further classification. (Rest of abstract omitted due to arXiv abstract limit)

Casper Hansen, Christian Hansen, Lucas Chaves Lima

Most fact checking models for automatic fake news detection are based on reasoning: given a claim with associated evidence, the models aim to estimate the claim veracity based on the supporting or refuting content within the evidence. When these models perform well, it is generally assumed to be due to the models having learned to reason over the evidence with regards to the claim. In this paper, we investigate this assumption of reasoning, by exploring the relationship and importance of both claim and evidence. Surprisingly, we find on political fact checking datasets that most often the highest effectiveness is obtained by utilizing only the evidence, as the impact of including the claim is either negligible or harmful to the effectiveness. This highlights an important problem in what constitutes evidence in existing approaches for automatic fake news detection.

Anneke Meyer, Suhita Ghosh, Daniel Schindele et al.

Various convolutional neural network (CNN) based concepts have been introduced for the prostate's automatic segmentation and its coarse subdivision into transition zone (TZ) and peripheral zone (PZ). However, when targeting a fine-grained segmentation of TZ, PZ, distal prostatic urethra (DPU) and the anterior fibromuscular stroma (AFS), the task becomes more challenging and has not yet been solved at the level of human performance. One reason might be the insufficient amount of labeled data for supervised training. Therefore, we propose to apply a semi-supervised learning (SSL) technique named uncertainty-aware temporal self-learning (UATS) to overcome the expensive and time-consuming manual ground truth labeling. We combine the SSL techniques temporal ensembling and uncertainty-guided self-learning to benefit from unlabeled images, which are often readily available. Our method significantly outperforms the supervised baseline and obtained a Dice coefficient (DC) of up to 78.9% , 87.3%, 75.3%, 50.6% for TZ, PZ, DPU and AFS, respectively. The obtained results are in the range of human inter-rater performance for all structures. Moreover, we investigate the method's robustness against noise and demonstrate the generalization capability for varying ratios of labeled data and on other challenging tasks, namely the hippocampus and skin lesion segmentation. UATS achieved superiority segmentation quality compared to the supervised baseline, particularly for minimal amounts of labeled data.

Christian Hansen, Casper Hansen, Jakob Grue Simonsen et al.

Semantic hashing represents documents as compact binary vectors (hash codes) and allows both efficient and effective similarity search in large-scale information retrieval. The state of the art has primarily focused on learning hash codes that improve similarity search effectiveness, while assuming a brute-force linear scan strategy for searching over all the hash codes, even though much faster alternatives exist. One such alternative is multi-index hashing, an approach that constructs a smaller candidate set to search over, which depending on the distribution of the hash codes can lead to sub-linear search time. In this work, we propose Multi-Index Semantic Hashing (MISH), an unsupervised hashing model that learns hash codes that are both effective and highly efficient by being optimized for multi-index hashing. We derive novel training objectives, which enable to learn hash codes that reduce the candidate sets produced by multi-index hashing, while being end-to-end trainable. In fact, our proposed training objectives are model agnostic, i.e., not tied to how the hash codes are generated specifically in MISH, and are straight-forward to include in existing and future semantic hashing models. We experimentally compare MISH to state-of-the-art semantic hashing baselines in the task of document similarity search. We find that even though multi-index hashing also improves the efficiency of the baselines compared to a linear scan, they are still upwards of 33% slower than MISH, while MISH is still able to obtain state-of-the-art effectiveness.

Christian Hansen, Casper Hansen, Jakob Grue Simonsen et al.

When reasoning about tasks that involve large amounts of data, a common approach is to represent data items as objects in the Hamming space where operations can be done efficiently and effectively. Object similarity can then be computed by learning binary representations (hash codes) of the objects and computing their Hamming distance. While this is highly efficient, each bit dimension is equally weighted, which means that potentially discriminative information of the data is lost. A more expressive alternative is to use real-valued vector representations and compute their inner product; this allows varying the weight of each dimension but is many magnitudes slower. To fix this, we derive a new way of measuring the dissimilarity between two objects in the Hamming space with binary weighting of each dimension (i.e., disabling bits): we consider a field-agnostic dissimilarity that projects the vector of one object onto the vector of the other. When working in the Hamming space, this results in a novel projected Hamming dissimilarity, which by choice of projection, effectively allows a binary importance weighting of the hash code of one object through the hash code of the other. We propose a variational hashing model for learning hash codes optimized for this projected Hamming dissimilarity, and experimentally evaluate it in collaborative filtering experiments. The resultant hash codes lead to effectiveness gains of up to +7% in NDCG and +14% in MRR compared to state-of-the-art hashing-based collaborative filtering baselines, while requiring no additional storage and no computational overhead compared to using the Hamming distance.

Oleksii Bashkanov, Anneke Meyer, Daniel Schindele et al.

Recent studies demonstrated the eligibility of convolutional neural networks (CNNs) for solving the image registration problem. CNNs enable faster transformation estimation and greater generalization capability needed for better support during medical interventions. Conventional fully-supervised training requires a lot of high-quality ground truth data such as voxel-to-voxel transformations, which typically are attained in a too tedious and error-prone manner. In our work, we use weakly-supervised learning, which optimizes the model indirectly only via segmentation masks that are a more accessible ground truth than the deformation fields. Concerning the weak supervision, we investigate two segmentation similarity measures: multiscale Dice similarity coefficient (mDSC) and the similarity between segmentation-derived signed distance maps (SDMs). We show that the combination of mDSC and SDM similarity measures results in a more accurate and natural transformation pattern together with a stronger gradient coverage. Furthermore, we introduce an auxiliary input to the neural network for the prior information about the prostate location in the MR sequence, which mostly is available preoperatively. This approach significantly outperforms the standard two-input models. With weakly labelled MR-TRUS prostate data, we showed registration quality comparable to the state-of-the-art deep learning-based method.

Dongsheng Wang, Casper Hansen, Lucas Chaves Lima et al.

The state of the art in learning meaningful semantic representations of words is the Transformer model and its attention mechanisms. Simply put, the attention mechanisms learn to attend to specific parts of the input dispensing recurrence and convolutions. While some of the learned attention heads have been found to play linguistically interpretable roles, they can be redundant or prone to errors. We propose a method to guide the attention heads towards roles identified in prior work as important. We do this by defining role-specific masks to constrain the heads to attend to specific parts of the input, such that different heads are designed to play different roles. Experiments on text classification and machine translation using 7 different datasets show that our method outperforms competitive attention-based, CNN, and RNN baselines.

Lucas Chaves Lima, Casper Hansen, Christian Hansen et al.

This report describes the participation of two Danish universities, University of Copenhagen and Aalborg University, in the international search engine competition on COVID-19 (the 2020 TREC-COVID Challenge) organised by the U.S. National Institute of Standards and Technology (NIST) and its Text Retrieval Conference (TREC) division. The aim of the competition was to find the best search engine strategy for retrieving precise biomedical scientific information on COVID-19 from the largest, at that point in time, dataset of curated scientific literature on COVID-19 -- the COVID-19 Open Research Dataset (CORD-19). CORD-19 was the result of a call to action to the tech community by the U.S. White House in March 2020, and was shortly thereafter posted on Kaggle as an AI competition by the Allen Institute for AI, the Chan Zuckerberg Initiative, Georgetown University's Center for Security and Emerging Technology, Microsoft, and the National Library of Medicine at the US National Institutes of Health. CORD-19 contained over 200,000 scholarly articles (of which more than 100,000 were with full text) about COVID-19, SARS-CoV-2, and related coronaviruses, gathered from curated biomedical sources. The TREC-COVID challenge asked for the best way to (a) retrieve accurate and precise scientific information, in response to some queries formulated by biomedical experts, and (b) rank this information decreasingly by its relevance to the query. In this document, we describe the TREC-COVID competition setup, our participation to it, and our resulting reflections and lessons learned about the state-of-art technology when faced with the acute task of retrieving precise scientific information from a rapidly growing corpus of literature, in response to highly specialised queries, in the middle of a pandemic.

Anneke Meyer, Grzegorz Chlebus, Marko Rak et al.

Background and Objective: Accurate and reliable segmentation of the prostate gland in MR images can support the clinical assessment of prostate cancer, as well as the planning and monitoring of focal and loco-regional therapeutic interventions. Despite the availability of multi-planar MR scans due to standardized protocols, the majority of segmentation approaches presented in the literature consider the axial scans only. Methods: We propose an anisotropic 3D multi-stream CNN architecture, which processes additional scan directions to produce a higher-resolution isotropic prostate segmentation. We investigate two variants of our architecture, which work on two (dual-plane) and three (triple-plane) image orientations, respectively. We compare them with the standard baseline (single-plane) used in literature, i.e., plain axial segmentation. To realize a fair comparison, we employ a hyperparameter optimization strategy to select optimal configurations for the individual approaches. Results: Training and evaluation on two datasets spanning multiple sites obtain statistical significant improvement over the plain axial segmentation ($p<0.05$ on the Dice similarity coefficient). The improvement can be observed especially at the base ($0.898$ single-plane vs. $0.906$ triple-plane) and apex ($0.888$ single-plane vs. $0.901$ dual-plane). Conclusion: This study indicates that models employing two or three scan directions are superior to plain axial segmentation. The knowledge of precise boundaries of the prostate is crucial for the conservation of risk structures. Thus, the proposed models have the potential to improve the outcome of prostate cancer diagnosis and therapies.

Casper Hansen, Christian Hansen, Jakob Grue Simonsen et al.

Semantic Hashing is a popular family of methods for efficient similarity search in large-scale datasets. In Semantic Hashing, documents are encoded as short binary vectors (i.e., hash codes), such that semantic similarity can be efficiently computed using the Hamming distance. Recent state-of-the-art approaches have utilized weak supervision to train better performing hashing models. Inspired by this, we present Semantic Hashing with Pairwise Reconstruction (PairRec), which is a discrete variational autoencoder based hashing model. PairRec first encodes weakly supervised training pairs (a query document and a semantically similar document) into two hash codes, and then learns to reconstruct the same query document from both of these hash codes (i.e., pairwise reconstruction). This pairwise reconstruction enables our model to encode local neighbourhood structures within the hash code directly through the decoder. We experimentally compare PairRec to traditional and state-of-the-art approaches, and obtain significant performance improvements in the task of document similarity search.

Christian Hansen, Casper Hansen, Jakob Grue Simonsen et al.

We study whether it is possible to infer if a news headline is true or false using only the movement of the human eyes when reading news headlines. Our study with 55 participants who are eye-tracked when reading 108 news headlines (72 true, 36 false) shows that false headlines receive statistically significantly less visual attention than true headlines. We further build an ensemble learner that predicts news headline factuality using only eye-tracking measurements. Our model yields a mean AUC of 0.688 and is better at detecting false than true headlines. Through a model analysis, we find that eye-tracking 25 users when reading 3-6 headlines is sufficient for our ensemble learner.

Casper Hansen, Christian Hansen, Jakob Grue Simonsen et al.

Content-aware recommendation approaches are essential for providing meaningful recommendations for \textit{new} (i.e., \textit{cold-start}) items in a recommender system. We present a content-aware neural hashing-based collaborative filtering approach (NeuHash-CF), which generates binary hash codes for users and items, such that the highly efficient Hamming distance can be used for estimating user-item relevance. NeuHash-CF is modelled as an autoencoder architecture, consisting of two joint hashing components for generating user and item hash codes. Inspired from semantic hashing, the item hashing component generates a hash code directly from an item's content information (i.e., it generates cold-start and seen item hash codes in the same manner). This contrasts existing state-of-the-art models, which treat the two item cases separately. The user hash codes are generated directly based on user id, through learning a user embedding matrix. We show experimentally that NeuHash-CF significantly outperforms state-of-the-art baselines by up to 12\% NDCG and 13\% MRR in cold-start recommendation settings, and up to 4\% in both NDCG and MRR in standard settings where all items are present while training. Our approach uses 2-4x shorter hash codes, while obtaining the same or better performance compared to the state of the art, thus consequently also enabling a notable storage reduction.

Gino Gulamhussene, Fabian Joeres, Marko Rak et al.

Purpose: We aim to develop a robust 4D MRI method for large FOVs enabling the extraction of irregular respiratory motion that is readily usable with all MRI machines and thus applicable to support a wide range of interventional settings. Method: We propose a 4D MRI reconstruction method to capture an arbitrary number of breathing states. It uses template updates in navigator slices and search regions for fast and robust vessel cross-section tracking. It captures FOVs of 255 mm x 320 mm x 228 mm at a spatial resolution of 1.82 mm x 1.82 mm x 4mm and temporal resolution of 200ms. A total of 37 4D MRIs of 13 healthy subjects were reconstructed to validate the method. A quantitative evaluation of the reconstruction rate and speed of both the new and baseline method was performed. Additionally, a study with ten radiologists was conducted to assess the subjective reconstruction quality of both methods. Results: Our results indicate improved mean reconstruction rates compared to the baseline method (79.4\% vs. 45.5\%) and improved mean reconstruction times (24s vs. 73s) per subject. Interventional radiologists perceive the reconstruction quality of our method as higher compared to the baseline (262.5 points vs. 217.5 points, p=0.02). Conclusions: Template updates are an effective and efficient way to increase 4D MRI reconstruction rates and to achieve better reconstruction quality. Search regions reduce reconstruction time. These improvements increase the applicability of 4D MRI as a base for seamless support of interventional image guidance in percutaneous interventions.

Isabelle Augenstein, Christina Lioma, Dongsheng Wang et al.

We contribute the largest publicly available dataset of naturally occurring factual claims for the purpose of automatic claim verification. It is collected from 26 fact checking websites in English, paired with textual sources and rich metadata, and labelled for veracity by human expert journalists. We present an in-depth analysis of the dataset, highlighting characteristics and challenges. Further, we present results for automatic veracity prediction, both with established baselines and with a novel method for joint ranking of evidence pages and predicting veracity that outperforms all baselines. Significant performance increases are achieved by encoding evidence, and by modelling metadata. Our best-performing model achieves a Macro F1 of 49.2%, showing that this is a challenging testbed for claim veracity prediction.

Casper Hansen, Christian Hansen, Stephen Alstrup et al.

Word embeddings predict a word from its neighbours by learning small, dense embedding vectors. In practice, this prediction corresponds to a semantic score given to the predicted word (or term weight). We present a novel model that, given a target word, redistributes part of that word's weight (that has been computed with word embeddings) across words occurring in similar contexts as the target word. Thus, our model aims to simulate how semantic meaning is shared by words occurring in similar contexts, which is incorporated into bag-of-words document representations. Experimental evaluation in an unsupervised setting against 8 state of the art baselines shows that our model yields the best micro and macro F1 scores across datasets of increasing difficulty.

Casper Hansen, Christian Hansen, Jakob Grue Simonsen et al.

Fast similarity search is a key component in large-scale information retrieval, where semantic hashing has become a popular strategy for representing documents as binary hash codes. Recent advances in this area have been obtained through neural network based models: generative models trained by learning to reconstruct the original documents. We present a novel unsupervised generative semantic hashing approach, \textit{Ranking based Semantic Hashing} (RBSH) that consists of both a variational and a ranking based component. Similarly to variational autoencoders, the variational component is trained to reconstruct the original document conditioned on its generated hash code, and as in prior work, it only considers documents individually. The ranking component solves this limitation by incorporating inter-document similarity into the hash code generation, modelling document ranking through a hinge loss. To circumvent the need for labelled data to compute the hinge loss, we use a weak labeller and thus keep the approach fully unsupervised. Extensive experimental evaluation on four publicly available datasets against traditional baselines and recent state-of-the-art methods for semantic hashing shows that RBSH significantly outperforms all other methods across all evaluated hash code lengths. In fact, RBSH hash codes are able to perform similarly to state-of-the-art hash codes while using 2-4x fewer bits.

Christian Hansen, Casper Hansen, Stephen Alstrup et al.

Recurrent neural networks (RNNs) can model natural language by sequentially 'reading' input tokens and outputting a distributed representation of each token. Due to the sequential nature of RNNs, inference time is linearly dependent on the input length, and all inputs are read regardless of their importance. Efforts to speed up this inference, known as 'neural speed reading', either ignore or skim over part of the input. We present Structural-Jump-LSTM: the first neural speed reading model to both skip and jump text during inference. The model consists of a standard LSTM and two agents: one capable of skipping single words when reading, and one capable of exploiting punctuation structure (sub-sentence separators (,:), sentence end symbols (.!?), or end of text markers) to jump ahead after reading a word. A comprehensive experimental evaluation of our model against all five state-of-the-art neural reading models shows that Structural-Jump-LSTM achieves the best overall floating point operations (FLOP) reduction (hence is faster), while keeping the same accuracy or even improving it compared to a vanilla LSTM that reads the whole text.

Casper Hansen, Christian Hansen, Stephen Alstrup et al.

Automatic fact-checking systems detect misinformation, such as fake news, by (i) selecting check-worthy sentences for fact-checking, (ii) gathering related information to the sentences, and (iii) inferring the factuality of the sentences. Most prior research on (i) uses hand-crafted features to select check-worthy sentences, and does not explicitly account for the recent finding that the top weighted terms in both check-worthy and non-check-worthy sentences are actually overlapping [15]. Motivated by this, we present a neural check-worthiness sentence ranking model that represents each word in a sentence by \textit{both} its embedding (aiming to capture its semantics) and its syntactic dependencies (aiming to capture its role in modifying the semantics of other terms in the sentence). Our model is an end-to-end trainable neural network for check-worthiness ranking, which is trained on large amounts of unlabelled data through weak supervision. Thorough experimental evaluation against state of the art baselines, with and without weak supervision, shows our model to be superior at all times (+13% in MAP and +28% at various Precision cut-offs from the best baseline with statistical significance). Empirical analysis of the use of weak supervision, word embedding pretraining on domain-specific data, and the use of syntactic dependencies of our model reveals that check-worthy sentences contain notably more identical syntactic dependencies than non-check-worthy sentences.

Rastin Matin, Casper Hansen, Christian Hansen et al.

Corporate distress models typically only employ the numerical financial variables in the firms' annual reports. We develop a model that employs the unstructured textual data in the reports as well, namely the auditors' reports and managements' statements. Our model consists of a convolutional recurrent neural network which, when concatenated with the numerical financial variables, learns a descriptive representation of the text that is suited for corporate distress prediction. We find that the unstructured data provides a statistically significant enhancement of the distress prediction performance, in particular for large firms where accurate predictions are of the utmost importance. Furthermore, we find that auditors' reports are more informative than managements' statements and that a joint model including both managements' statements and auditors' reports displays no enhancement relative to a model including only auditors' reports. Our model demonstrates a direct improvement over existing state-of-the-art models.

Christian Hansen, Casper Hansen, Niklas Hjuler et al.

The analysis of log data generated by online educational systems is an important task for improving the systems, and furthering our knowledge of how students learn. This paper uses previously unseen log data from Edulab, the largest provider of digital learning for mathematics in Denmark, to analyse the sessions of its users, where 1.08 million student sessions are extracted from a subset of their data. We propose to model students as a distribution of different underlying student behaviours, where the sequence of actions from each session belongs to an underlying student behaviour. We model student behaviour as Markov chains, such that a student is modelled as a distribution of Markov chains, which are estimated using a modified k-means clustering algorithm. The resulting Markov chains are readily interpretable, and in a qualitative analysis around 125,000 student sessions are identified as exhibiting unproductive student behaviour. Based on our results this student representation is promising, especially for educational systems offering many different learning usages, and offers an alternative to common approaches like modelling student behaviour as a single Markov chain often done in the literature.

Victor Chernozhukov, Denis Chetverikov, Mert Demirer et al.

Chernozhukov, Chetverikov, Demirer, Duflo, Hansen, and Newey (2016) provide a generic double/de-biased machine learning (DML) approach for obtaining valid inferential statements about focal parameters, using Neyman-orthogonal scores and cross-fitting, in settings where nuisance parameters are estimated using a new generation of nonparametric fitting methods for high-dimensional data, called machine learning methods. In this note, we illustrate the application of this method in the context of estimating average treatment effects (ATE) and average treatment effects on the treated (ATTE) using observational data. A more general discussion and references to the existing literature are available in Chernozhukov, Chetverikov, Demirer, Duflo, Hansen, and Newey (2016).

Victor Chernozhukov, Denis Chetverikov, Mert Demirer et al.

Most modern supervised statistical/machine learning (ML) methods are explicitly designed to solve prediction problems very well. Achieving this goal does not imply that these methods automatically deliver good estimators of causal parameters. Examples of such parameters include individual regression coefficients, average treatment effects, average lifts, and demand or supply elasticities. In fact, estimates of such causal parameters obtained via naively plugging ML estimators into estimating equations for such parameters can behave very poorly due to the regularization bias. Fortunately, this regularization bias can be removed by solving auxiliary prediction problems via ML tools. Specifically, we can form an orthogonal score for the target low-dimensional parameter by combining auxiliary and main ML predictions. The score is then used to build a de-biased estimator of the target parameter which typically will converge at the fastest possible 1/root(n) rate and be approximately unbiased and normal, and from which valid confidence intervals for these parameters of interest may be constructed. The resulting method thus could be called a "double ML" method because it relies on estimating primary and auxiliary predictive models. In order to avoid overfitting, our construction also makes use of the K-fold sample splitting, which we call cross-fitting. This allows us to use a very broad set of ML predictive methods in solving the auxiliary and main prediction problems, such as random forest, lasso, ridge, deep neural nets, boosted trees, as well as various hybrids and aggregators of these methods.

Alexandre Belloni, Victor Chernozhukov, Ivan Fernández-Val et al.

In this paper, we provide efficient estimators and honest confidence bands for a variety of treatment effects including local average (LATE) and local quantile treatment effects (LQTE) in data-rich environments. We can handle very many control variables, endogenous receipt of treatment, heterogeneous treatment effects, and function-valued outcomes. Our framework covers the special case of exogenous receipt of treatment, either conditional on controls or unconditionally as in randomized control trials. In the latter case, our approach produces efficient estimators and honest bands for (functional) average treatment effects (ATE) and quantile treatment effects (QTE). To make informative inference possible, we assume that key reduced form predictive relationships are approximately sparse. This assumption allows the use of regularization and selection methods to estimate those relations, and we provide methods for post-regularization and post-selection inference that are uniformly valid (honest) across a wide-range of models. We show that a key ingredient enabling honest inference is the use of orthogonal or doubly robust moment conditions in estimating certain reduced form functional parameters. We illustrate the use of the proposed methods with an application to estimating the effect of 401(k) eligibility and participation on accumulated assets.