We consider learning the structures of Gaussian latent tree models with vector observations when a subset of them are arbitrarily corrupted. First, we present the sample complexities of Recursive Grouping (RG) and Chow-Liu Recursive Grouping (CLRG) without the assumption that the effective depth is bounded in the number of observed nodes, significantly generalizing the results in Choi et al. (2011). We show that Chow-Liu initialization in CLRG greatly reduces the sample complexity of RG from being exponential in the diameter of the tree to only logarithmic in the diameter for the hidden Markov model (HMM). Second, we robustify RG, CLRG, Neighbor Joining (NJ) and Spectral NJ (SNJ) by using the truncated inner product. These robustified algorithms can tolerate a number of corruptions up to the square root of the number of clean samples. Finally, we derive the first known instance-dependent impossibility result for structure learning of latent trees. The optimalities of the robust version of CLRG and NJ are verified by comparing their sample complexities and the impossibility result.

The success of reinforcement learning (RL) algorithms in large-scale, complex tasks depends on forming useful representations of the environment with which the algorithms interact. Feature selection and feature learning has long been an important subdomain of RL, and with the advent of deep reinforcement learning there has been much recent interest in understanding and improving the representations learnt by RL agents. Much of the work in representation learning has taken place from the perspective of auxiliary tasks [Jaderberg et al., 2017, Bellemare et al., 2017, Fedus et al., 2019]; in addition to the primary reinforcement learning task, the agent may attempt to predict and control additional aspects of the environment. Auxiliary tasks shape the agent's representation of the environment implicitly, typically via gradient descent on the additional learning objectives. As such, while auxiliary tasks continue to play an important role in improving the performance of deep RL algorithms, our understanding of the effects of auxiliary tasks on representations in RL is still in its infancy.

We present a novel framework for designing multiplierless kernel machines that can be used on resource-constrained platforms like intelligent edge devices. The framework uses a piecewise linear (PWL) approximation based on a margin propagation (MP) technique and uses only addition/subtraction, shift, comparison, and register underflow/overflow operations. We propose a hardware-friendly MP-based inference and online training algorithm that has been optimized for a Field Programmable Gate Array (FPGA) platform. Our FPGA implementation eliminates the need for DSP units and reduces the number of LUTs. By reusing the same hardware for inference and training, we show that the platform can overcome classification errors and local minima artifacts that result from the MP approximation. Using the FPGA platform, we also show that the proposed multiplierless MP-kernel machine demonstrates superior performance in terms of power, performance, and area compared to other comparable implementations.

This is a tutorial and survey paper for nonlinear dimensionality and feature extraction methods which are based on the Laplacian of graph of data. We first introduce adjacency matrix, definition of Laplacian matrix, and the interpretation of Laplacian. Then, we cover the cuts of graph and spectral clustering which applies clustering in a subspace of data. Different optimization variants of Laplacian eigenmap and its out-of-sample extension are explained. Thereafter, we introduce the locality preserving projection and its kernel variant as linear special cases of Laplacian eigenmap. Versions of graph embedding are then explained which are generalized versions of Laplacian eigenmap and locality preserving projection. Finally, diffusion map is introduced which is a method based on Laplacian of data and random walks on the data graph.

The simple gesture of pointing can greatly augment ones ability to comprehend states of the world based on observations. It triggers additional inferences relevant to ones task at hand. We model an agents update to its belief of the world based on individual observations using a partially observable Markov decision process (POMDP), a mainstream artificial intelligence (AI) model of how to act rationally according to beliefs formed through observation. On top of that, we model pointing as a communicative act between agents who have a mutual understanding that the pointed observation must be relevant and interpretable. Our model measures relevance by defining a Smithian Value of Information (SVI) as the utility improvement of the POMDP agent before and after receiving the pointing. We model that agents calculate SVI by using the cognitive theory of Smithian helping as a principle of coordinating separate beliefs for action prediction and action evaluation. We then import SVI into rational speech act (RSA) as the utility function of an utterance. These lead us to a pragmatic model of pointing allowing for contextually flexible interpretations. We demonstrate the power of our Smithian pointing model by extending the Wumpus world, a classic AI task where a hunter hunts a monster with only partial observability of the world. We add another agent as a guide who can only help by marking an observation already perceived by the hunter with a pointing or not, without providing new observations or offering any instrumental help. Our results show that this severely limited and overloaded communication nevertheless significantly improves the hunters performance. The advantage of pointing is indeed due to a computation of relevance based on Smithian helping, as it disappears completely when the task is too difficult or too easy for the guide to help.

Incomplete instances with various missing attributes in many real-world scenes have brought challenges to the classification task. There are some missing values imputation methods to fill the missing values with substitute values before classification. However, the separation between imputation and classification may lead to inferior performance since label information are ignored during imputation. Moreover, these imputation methods tend to initialize these missing values with strong prior assumptions, while the unreliability of such initialization is rarely considered. To tackle these problems, a novel semi-supervised conditional normalizing flow (SSCFlow) is proposed in this paper. SSCFlow explicitly utilizes the observed labels to facilitate the imputation and classification simultaneously by employing a semi-supervised algorithm to estimate the conditional probability density of missing values. Moreover, SSCFlow takes the initialized missing values as corrupted initial imputation and iteratively reconstructs their latent representations with an overcomplete denoising autoencoder to approximate the true conditional probability density of missing values. Experiments have been conducted with real-world datasets to demonstrate the robustness and efficiency of the proposed algorithm.

In this paper we present a novel method for learning hierarchical representations of Markov decision processes. Our method works by partitioning the state space into subsets, and defines subtasks for performing transitions between the partitions. We formulate the problem of partitioning the state space as an optimization problem that can be solved using gradient descent given a set of sampled trajectories, making our method suitable for high-dimensional problems with large state spaces. We empirically validate the method, by showing that it can successfully learn a useful hierarchical representation in a navigation domain. Once learned, the hierarchical representation can be used to solve different tasks in the given domain, thus generalizing knowledge across tasks.

We investigate the problem of Chinese Grammatical Error Correction (CGEC) and present a new framework named Tail-to-Tail (\textbf{TtT}) non-autoregressive sequence prediction to address the deep issues hidden in CGEC. Considering that most tokens are correct and can be conveyed directly from source to target, and the error positions can be estimated and corrected based on the bidirectional context information, thus we employ a BERT-initialized Transformer Encoder as the backbone model to conduct information modeling and conveying. Considering that only relying on the same position substitution cannot handle the variable-length correction cases, various operations such substitution, deletion, insertion, and local paraphrasing are required jointly. Therefore, a Conditional Random Fields (CRF) layer is stacked on the up tail to conduct non-autoregressive sequence prediction by modeling the token dependencies. Since most tokens are correct and easily to be predicted/conveyed to the target, then the models may suffer from a severe class imbalance issue. To alleviate this problem, focal loss penalty strategies are integrated into the loss functions. Moreover, besides the typical fix-length error correction datasets, we also construct a variable-length corpus to conduct experiments. Experimental results on standard datasets, especially on the variable-length datasets, demonstrate the effectiveness of TtT in terms of sentence-level Accuracy, Precision, Recall, and F1-Measure on tasks of error Detection and Correction.

Design-by-Analogy (DbA) is a design methodology, wherein new solutions are generated in a target domain based on inspiration drawn from a source domain through cross-domain analogical reasoning [1, 2, 3]. DbA is an active research area in engineering design and various methods and tools have been proposed to support the implement of its process [4, 5, 6, 7, 8]. Studies have shown that DbA can help designers mitigate design fixation [9] and improve design ideation outcomes [10]. Fig.1 presents an example of DbA applications [11]. This case aims to solve an engineering design problem: How might we rectify the loud sonic boom generated when trains travel at high speeds through tunnels in atmospheric conditions [11, 12]? For potential design solutions to this problem, engineers explored structures in other design fields than trains or in the nature that effectively "break" the sonic-boom effect. When looking into the nature, engineers discovered that kingfisher birds could slice through the air and dive into the water at extremely high speeds to catch prey while barely making a splash. By analogy, engineers re-designed the train's front-end nose to mimic the geometry of the kingfisher's beak. This analogical design reduced noise and eliminated tunnel booms.

Recent work has shown that not only decision trees (DTs) may not be interpretable but also proposed a polynomial-time algorithm for computing one PI-explanation of a DT. This paper shows that for a wide range of classifiers, globally referred to as decision graphs, and which include decision trees and binary decision diagrams, but also their multi-valued variants, there exist polynomial-time algorithms for computing one PI-explanation. In addition, the paper also proposes a polynomial-time algorithm for computing one contrastive explanation. These novel algorithms build on explanation graphs (XpG's). XpG's denote a graph representation that enables both theoretical and practically efficient computation of explanations for decision graphs. Furthermore, the paper pro- poses a practically efficient solution for the enumeration of explanations, and studies the complexity of deciding whether a given feature is included in some explanation. For the concrete case of decision trees, the paper shows that the set of all contrastive explanations can be enumerated in polynomial time. Finally, the experimental results validate the practical applicability of the algorithms proposed in the paper on a wide range of publicly available benchmarks.