Christopher Meek

Ansong Ni, Jeevana Priya Inala, Chenglong Wang et al.

Pretrained language models have shown superior performance on many natural language processing tasks, yet they still struggle at multi-step formal reasoning tasks like grade school math problems. One key challenge of finetuning them to solve such math reasoning problems is that many existing datasets only contain one reference solution for each problem, despite the fact that there are often alternative solutions resembling different reasoning paths to the final answer. This way, the finetuned models are biased towards the limited reference solutions, which limits their generalization to unseen examples. To mitigate this issue, we propose to let the model perform sampling during training and learn from both self-sampled fully-correct solutions, which yield the correct answer upon execution, and partially-correct solutions, whose intermediate state matches an intermediate state of a known correct solution. We show that our use of self-sampled correct and partially-correct solutions can benefit learning and help guide the sampling process, leading to more efficient exploration of the solution space. Additionally, we explore various training objectives to support learning from multiple solutions per example and find they greatly affect the performance. Experiments on two math reasoning datasets show the effectiveness of our method compared to learning from a single reference solution with MLE, where we improve PASS@100 from 35.5% to 44.5% for GSM8K, and 27.6% to 36.2% PASS@80 for MathQA. Such improvements are also consistent across different model sizes. Our code is available at https://github.com/microsoft/TraceCodegen.

Gabriel Poesia, Oleksandr Polozov, Vu Le et al.

Large pre-trained language models have been used to generate code,providing a flexible interface for synthesizing programs from natural language specifications. However, they often violate syntactic and semantic rules of their output language, limiting their practical usability. In this paper, we propose Synchromesh: a framework for substantially improving the reliability of pre-trained models for code generation. Synchromesh comprises two components. First, it retrieves few-shot examples from a training bank using Target Similarity Tuning (TST), a novel method for semantic example selection. TST learns to recognize utterances that describe similar target programs despite differences in surface natural language features. Then, Synchromesh feeds the examples to a pre-trained language model and samples programs using Constrained Semantic Decoding (CSD): a general framework for constraining the output to a set of valid programs in the target language. CSD leverages constraints on partial outputs to sample complete correct programs, and needs neither re-training nor fine-tuning of the language model. We evaluate our methods by synthesizing code from natural language descriptions using GPT-3 and Codex in three real-world languages: SQL queries, Vega-Lite visualizations and SMCalFlow programs. These domains showcase rich constraints that CSD is able to enforce, including syntax, scope, typing rules, and contextual logic. We observe substantial complementary gains from CSD and TST in prediction accuracy and in effectively preventing run-time errors.

Christopher Meek

Understanding prediction errors and determining how to fix them is critical to building effective predictive systems. In this paper, we delineate four types of prediction errors and demonstrate that these four types characterize all prediction errors. In addition, we describe potential remedies and tools that can be used to reduce the uncertainty when trying to determine the source of a prediction error and when trying to take action to remove a prediction errors.

Peter L. Spirtes, Christopher Meek, Thomas S. Richardson

We show that there is a general, informative and reliable procedure for discovering causal relations when, for all the investigator knows, both latent variables and selection bias may be at work. Given information about conditional independence and dependence relations between measured variables, even when latent variables and selection bias may be present, there are sufficient conditions for reliably concluding that there is a causal path from one variable to another, and sufficient conditions for reliably concluding when no such causal path exists.

Christopher Meek

This paper presents correct algorithms for answering the following two questions; (i) Does there exist a causal explanation consistent with a set of background knowledge which explains all of the observed independence facts in a sample? (ii) Given that there is such a causal explanation what are the causal relationships common to every such causal explanation?

David Maxwell Chickering, David Heckerman, Christopher Meek

Recently several researchers have investigated techniques for using data to learn Bayesian networks containing compact representations for the conditional probability distributions (CPDs) stored at each node. The majority of this work has concentrated on using decision-tree representations for the CPDs. In addition, researchers typically apply non-Bayesian (or asymptotically Bayesian) scoring functions such as MDL to evaluate the goodness-of-fit of networks to the data. In this paper we investigate a Bayesian approach to learning Bayesian networks that contain the more general decision-graph representations of the CPDs. First, we describe how to evaluate the posterior probability that is, the Bayesian score of such a network, given a database of observed cases. Second, we describe various search spaces that can be used, in conjunction with a scoring function and a search procedure, to identify one or more high-scoring networks. Finally, we present an experimental evaluation of the search spaces, using a greedy algorithm and a Bayesian scoring function.

Andrew Zimdars, David Maxwell Chickering, Christopher Meek

We treat collaborative filtering as a univariate time series estimation problem: given a user's previous votes, predict the next vote. We describe two families of methods for transforming data to encode time order in ways amenable to off-the-shelf classification and density estimation tools, and examine the results of using these approaches on several real-world data sets. The improvements in predictive accuracy we realize recommend the use of other predictive algorithms that exploit the temporal order of data.

Bo Thiesson, David Maxwell Chickering, David Heckerman et al.

We express the classic ARMA time-series model as a directed graphical model. In doing so, we find that the deterministic relationships in the model make it effectively impossible to use the EM algorithm for learning model parameters. To remedy this problem, we replace the deterministic relationships with Gaussian distributions having a small variance, yielding the stochastic ARMA (ARMA) model. This modification allows us to use the EM algorithm to learn parmeters and to forecast,even in situations where some data is missing. This modification, in conjunction with the graphicalmodel approach, also allows us to include cross predictors in situations where there are multiple times series and/or additional nontemporal covariates. More surprising,experiments suggest that the move to stochastic ARMA yields improved accuracy through better smoothing. We demonstrate improvements afforded by cross prediction and better smoothing on real data.