The Bezier simplex fitting is a novel data modeling technique which exploits geometric structures of data to approximate the Pareto front of multi-objective optimization problems. There are two fitting methods based on different sampling strategies. The inductive skeleton fitting employs a stratified subsampling from each skeleton of a simplex, whereas the all-at-once fitting uses a non-stratified sampling which treats a simplex as a whole. In this paper, we analyze the asymptotic risks of those B\'ezier simplex fitting methods and derive the optimal subsample ratio for the inductive skeleton fitting. It is shown that the inductive skeleton fitting with the optimal ratio has a smaller risk when the degree of a Bezier simplex is less than three. Those results are verified numerically under small to moderate sample sizes. In addition, we provide two complementary applications of our theory: a generalized location problem and a multi-objective hyper-parameter tuning of the group lasso. The former can be represented by a Bezier simplex of degree two where the inductive skeleton fitting outperforms. The latter can be represented by a Bezier simplex of degree three where the all-at-once fitting gets an advantage.

Solving complex, temporally-extended tasks is a long-standing problem in reinforcement learning (RL). We hypothesize that one critical element of solving such problems is the notion of compositionality. With the ability to learn concepts and sub-skills that can be composed to solve longer tasks, i.e. hierarchical RL, we can acquire temporally-extended behaviors. However, acquiring effective yet general abstractions for hierarchical RL is remarkably challenging. In this paper, we propose to use language as the abstraction, as it provides unique compositional structure, enabling fast learning and combinatorial generalization, while retaining tremendous flexibility, making it suitable for a variety of problems. Our approach learns an instruction-following low-level policy and a high-level policy that can reuse abstractions across tasks, in essence, permitting agents to reason using structured language. To study compositional task learning, we introduce an open-source object interaction environment built using the MuJoCo physics engine and the CLEVR engine. We find that, using our approach, agents can learn to solve to diverse, temporally-extended tasks such as object sorting and multi-object rearrangement, including from raw pixel observations. Our analysis find that the compositional nature of language is critical for learning diverse sub-skills and systematically generalizing to new sub-skills in comparison to non-compositional abstractions that use the same supervision.

Annotating large unlabeled datasets can be a major bottleneck for machine learning applications. We introduce a scheme for inferring labels of unlabeled data at a fraction of the cost of labeling the entire dataset. We refer to the scheme as greedy split and label exploration (GSAL). GSAL greedily queries an oracle (or human labeler) and partitions a dataset to find data subsets that have mostly the same label. GSAL can then infer labels by majority vote of the known labels in each subset. GSAL makes the decision to split or label from a subset by maximizing a lower bound on the expected number of correctly labeled examples. GSAL improves upon existing hierarchical labeling schemes by using supervised models to partition the data, therefore avoiding reliance on unsupervised clustering methods that may not accurately group data by label. We design GSAL with strategies to avoid bias that could be introduced through this adaptive partitioning. We evaluate GSAL on labeling of three datasets and find that it outperforms existing strategies for adaptive labeling.

The concept of causality has a controversial history. The question of whether it is possible to represent and address causal problems with probability theory, or if fundamentally new mathematics such as the do calculus is required has been hotly debated, e.g. Pearl (2001) states "the building blocks of our scientific and everyday knowledge are elementary facts such as "mud does not cause rain" and "symptoms do not cause disease" and those facts, strangely enough, cannot be expressed in the vocabulary of probability calculus". This has lead to a dichotomy between advocates of causal graphical modeling and the do calculus, and researchers applying Bayesian methods. In this paper we demonstrate that, while it is critical to explicitly model our assumptions on the impact of intervening in a system, provided we do so, estimating causal effects can be done entirely within the standard Bayesian paradigm. The invariance assumptions underlying causal graphical models can be encoded in ordinary Probabilistic graphical models, allowing causal estimation with Bayesian statistics, equivalent to the do calculus. Elucidating the connections between these approaches is a key step toward enabling the insights provided by each to be combined to solve real problems.

In this work, we explain the working mechanism of MixUp in terms of adversarial training. We introduce a new class of adversarial training schemes, which we refer to as directional adversarial training, or DAT. In a nutshell, a DAT scheme perturbs a training example in the direction of another example but keeps its original label as the training target. We prove that MixUp is equivalent to a special subclass of DAT, in that it has the same expected loss function and corresponds to the same optimization problem asymptotically. This understanding not only serves to explain the effectiveness of MixUp, but also reveals a more general family of MixUp schemes, which we call Untied MixUp. We prove that the family of Untied MixUp schemes is equivalent to the entire class of DAT schemes. We establish empirically the existence of Untied Mixup schemes which improve upon MixUp.

Cephalometric tracing method is usually used in orthodontic diagnosis and treat-ment planning. In this paper, we propose a deep learning based framework to au-tomatically detect anatomical landmarks in cephalometric X-ray images. We train the deep encoder-decoder for landmark detection, and combine global landmark configuration with local high-resolution feature responses. The proposed frame-work is based on 2-stage u-net, regressing the multi-channel heatmaps for land-mark detection. In this framework, we embed attention mechanism with global stage heatmaps, guiding the local stage inferring, to regress the local heatmap patches in a high resolution. Besides, the Expansive Exploration strategy im-proves robustness while inferring, expanding the searching scope without in-creasing model complexity. We have evaluated our framework in the most wide-ly-used public dataset of landmark detection in cephalometric X-ray images. With less computation and manually tuning, our framework achieves state-of-the-art results.

We present a novel reinforcement learning-based natural media painting algorithm. Our goal is to reproduce a reference image using brush strokes and we encode the objective through observations. Our formulation takes into account that the distribution of the reward in the action space is sparse and training a reinforcement learning algorithm from scratch can be difficult. We present an approach that combines self-supervised learning and reinforcement learning to effectively transfer negative samples into positive ones and change the reward distribution. We demonstrate the benefits of our painting agent to reproduce reference images with brush strokes. The training phase takes about one hour and the runtime algorithm takes about 30 seconds on a GTX1080 GPU reproducing a 1000 800 image with 20,000 strokes.

Conebeam CT using a circular trajectory is quite often used for various applications due to its relative simple geometry. For conebeam geometry, Feldkamp, Davis and Kress algorithm is regarded as the standard reconstruction method, but this algorithm suffers from so-called conebeam artifacts as the cone angle increases. Various model-based iterative reconstruction methods have been developed to reduce the cone-beam artifacts, but these algorithms usually require multiple applications of computational expensive forward and backprojections. In this paper, we develop a novel deep learning approach for accurate conebeam artifact removal. In particular, our deep network, designed on the differentiated backprojection domain, performs a data-driven inversion of an ill-posed deconvolution problem associated with the Hilbert transform. The reconstruction results along the coronal and sagittal directions are then combined using a spectral blending technique to minimize the spectral leakage. Experimental results show that our method outperforms the existing iterative methods despite significantly reduced runtime complexity.

It is common practice in using regression type models for inferring causal effects, that inferring the correct causal relationship requires extra covariates are included or ``adjusted for''. Without performing this adjustment erroneous causal effects can be inferred. Given this phenomenon it is common practice to include as many covariates as possible, however such advice comes unstuck in the presence of M-bias. M-Bias is a problem in causal inference where the correct estimation of treatment effects requires that certain variables are not adjusted for i.e. are simply neglected from inclusion in the model. This issue caused a storm of controversy in 2009 when Rubin, Pearl and others disagreed about if it could be problematic to include additional variables in models when inferring causal effects. This paper makes two contributions to this issue. Firstly we provide a Bayesian solution to the M-Bias problem. The solution replicates Pearl's solution, but consistent with Rubin's advice we condition on all variables. Secondly the fact that we are able to offer a solution to this problem in Bayesian terms shows that it is indeed possible to represent causal relationships within the Bayesian paradigm, albeit in an extended space. We make several remarks on the similarities and differences between causal graphical models which implement the do-calculus and probabilistic graphical models which enable Bayesian statistics. We hope this work will stimulate more research on unifying Pearl's causal calculus using causal graphical models with traditional Bayesian statistics and probabilistic graphical models.

Activity recognition is the ability to identify and recognize the action or goals of the agent. The agent can be any object or entity that performs action that has end goals. The agents can be a single agent performing the action or group of agents performing the actions or having some interaction. Human activity recognition has gained popularity due to its demands in many practical applications such as entertainment, healthcare, simulations and surveillance systems. Vision based activity recognition is gaining advantage as it does not require any human intervention or physical contact with humans. Moreover, there are set of cameras that are networked with the intention to track and recognize the activities of the agent. Traditional applications that were required to track or recognize human activities made use of wearable devices. However, such applications require physical contact of the person. To overcome such challenges, vision based activity recognition system can be used, which uses a camera to record the video and a processor that performs the task of recognition. The work is implemented in two stages. In the first stage, an approach for the Implementation of Activity recognition is proposed using background subtraction of images, followed by 3D- Convolutional Neural Networks. The impact of using Background subtraction prior to 3D-Convolutional Neural Networks has been reported. In the second stage, the work is further extended and implemented on Raspberry Pi, that can be used to record a stream of video, followed by recognizing the activity that was involved in the video. Thus, a proof-of-concept for activity recognition using small, IoT based device, is provided, which can enhance the system and extend its applications in various forms like, increase in portability, networking, and other capabilities of the device.