We define and study the problem of modular concept learning, that is, learning a concept that is a cross product of component concepts. If an element's membership in a concept depends solely on it's membership in the components, learning the concept as a whole can be reduced to learning the components. We analyze this problem with respect to different types of oracle interfaces, defining different sets of queries. If a given oracle interface cannot answer questions about the components, learning can be difficult, even when the components are easy to learn with the same type of oracle queries. While learning from superset queries is easy, learning from membership, equivalence, or subset queries is harder. However, we show that these problems become tractable when oracles are given a positive example and are allowed to ask membership queries. Keywords: Inductive Synthesis, Query-Based Learning, Modularity 1 Introduction Inductive synthesis or inductive learning is the synthesis of programs (concepts) from examples or other observations. Inductive synthesis has found application in formal methods, program analysis, software engineering, and related areas, for problems such as invariant generation (e.g.

Programming by example is the problem of synthesizing a program from a small set of input / output pairs. Recent works applying machine learning methods to this task show promise, but are typically reliant on generating synthetic examples for training. A particular challenge lies in generating meaningful sets of inputs and outputs, which well-characterize a given program and accurately demonstrate its behavior. Where examples used for testing are generated by the same method as training data then the performance of a model may be partly reliant on this similarity. In this paper we introduce a novel approach using an SMT solver to synthesize inputs which cover a diverse set of behaviors for a given program. We carry out a case study comparing this method to existing synthetic data generation procedures in the literature, and find that data generated using our approach improves both the discriminatory power of example sets and the ability of trained machine learning models to generalize to unfamiliar data.

Recent years have witnessed growing interest in machine learning-based models and techniques for low-dose X-ray CT (LDCT) imaging tasks. The methods can typically be categorized into supervised learning methods and unsupervised or model-based learning methods. Supervised learning methods have recently shown success in image restoration tasks. However, they often rely on large training sets. Model-based learning methods such as dictionary or transform learning do not require large or paired training sets and often have good generalization properties, since they learn general properties of CT image sets.

Autonomous vehicles generate a lot of raw (unlabeled) data every minute. But only a small fraction of that data can be labeled manually. Ashesh focuses on how we leverage unlabeled data for tasks on perception and prediction in a self-supervised manner. He touches on a few unique ways to achieve this goal in the AV land, including cross-modal self-supervised learning, in which one modality can serve as a learning signal for another modality without the need for labeling. Another approach he touches on is using outputs from large-scale optimization as a learning signal to train neural networks, which is done by mimicking their outputs but running in real-time on the AV. Ashesh further explores how we can leverage the Lyft fleet to oversample the long tail events and, hence, learn the long tail.

In many applications of machine learning, the training and test set data come from different distributions, or domains. A number of domain generalization strategies have been introduced with the goal of achieving good performance on out-of-distribution data. In this paper, we propose an adversarial approach to the problem. We propose a process that enforces pair-wise domain invariance while training a feature extractor over a diverse set of domains. We show that this process ensures invariance to any distribution that can be expressed as a mixture of the training domains. Following this insight, we then introduce an adversarial approach in which pair-wise divergences are estimated and minimized. Experiments on two domain generalization benchmarks for object recognition (i.e., PACS and VLCS) show that the proposed method yields higher average accuracy on the target domains in comparison to previously introduced adversarial strategies, as well as recently proposed methods based on learning invariant representations.

If you're a beginner, machine learning can be confusing for you– how to choose which algorithms to use, from the apparently limitless options, and how to know which one will provide the right predictions (data outputs). The machine learning is a way for computers to run various algorithms without direct human oversight in order to learn from data. So, just before starting with Machine learning algorithms, let's have a look at types of Machine learning which clarify these algorithms. Machine learning algorithms are programs that can learn from data and improve from experience, without human interference. Learning tasks may include learning the function that drafts the input to the output, learning the hidden structure in unlabeled data; or'instance-based learning', where a class label is produced for a new instance by analyzing the new instance (row) to instances from the training data, which were stored in memory. Machine Learning algorithm is an evolution of the regular algorithm.

We present a machine-checked, formal proof of PAC learnability of the concept class of decision stumps. A formal proof has every step checked and justified using fundamental axioms of mathematics. We construct and check our proof using the Lean theorem prover. Though such a proof appears simple, a few analytic and measure-theoretic subtleties arise when carrying it out fully formally. We explain how we can cleanly separate out the parts that deal with these subtleties by using Lean features and a category theoretic construction called the Giry monad.

For joint inference over multiple variables, a variety of structured prediction techniques have been developed to model correlations among variables and thereby improve predictions. However, many classical approaches suffer from one of two primary drawbacks: they either lack the ability to model high-order correlations among variables while maintaining computationally tractable inference, or they do not allow to explicitly model known correlations. To address this shortcoming, we introduce `Graph Structured Prediction Energy Networks,' for which we develop inference techniques that allow to both model explicit local and implicit higher-order correlations while maintaining tractability of inference. We apply the proposed method to tasks from the natural language processing and computer vision domain and demonstrate its general utility.

In this paper, we proposed a general framework for data poisoning attacks to graph-based semi-supervised learning (G-SSL). In this framework, we first unify different tasks, goals, and constraints into a single formula for data poisoning attack in G-SSL, then we propose two specialized algorithms to efficiently solve two important cases --- poisoning regression tasks under $\ell_2$-norm constraint and classification tasks under $\ell_0$-norm constraint. In the former case, we transform it into a non-convex trust region problem and show that our gradient-based algorithm with delicate initialization and update scheme finds the (globally) optimal perturbation. For the latter case, although it is an NP-hard integer programming problem, we propose a probabilistic solver that works much better than the classical greedy method. Lastly, we test our framework on real datasets and evaluate the robustness of G-SSL algorithms. For instance, on the MNIST binary classification problem (50000 training data with 50 labeled), flipping two labeled data is enough to make the model perform like random guess (around 50\% error).

Generative Adversarial Networks (GAN) have shown promising results on a wide variety of complex tasks. Recent experiments show adversarial training provides useful gradients to the generator that helps attain better performance. In this paper, we intend to theoretically analyze whether supervised learning with adversarial features can outperform sole supervision, or not. First, we show that supervised learning without adversarial features suffer from vanishing gradient issue in near optimal region. Second, we analyze how adversarial learning augmented with supervised signal mitigates this vanishing gradient issue. Finally, we prove our main result that shows supervised learning with adversarial features can be better than sole supervision (under some mild assumptions). We support our main result on two fronts (i) expected empirical risk and (ii) rate of convergence.