The Abstraction and Reasoning Corpus (ARC) was recently introduced by Fran\c{c}ois Chollet as a tool to measure broad intelligence in both humans and machines. It is very challenging, and the best approach in a Kaggle competition could only solve 20% of the tasks, relying on brute-force search for chains of hand-crafted transformations. In this paper, we present the first steps exploring an approach based on descriptive grid models and the Minimum Description Length (MDL) principle. The grid models describe the contents of a grid, and support both parsing grids and generating grids. The MDL principle is used to guide the search for good models, i.e. models that compress the grids the most. We report on our progress over a year, improving on the general approach and the models. Out of the 400 training tasks, our performance increased from 5 to 29 solved tasks, only using 30s computation time per task. Our approach not only predicts the output grids, but also outputs an intelligible model and explanations for how the model was incrementally built.

The principle of independent causal mechanisms (ICM) states that generative processes of real world data consist of independent modules which do not influence or inform each other. While this idea has led to fruitful developments in the field of causal inference, it is not widely-known in the NLP community. In this work, we argue that the causal direction of the data collection process bears nontrivial implications that can explain a number of published NLP findings, such as differences in semi-supervised learning (SSL) and domain adaptation (DA) performance across different settings. We categorize common NLP tasks according to their causal direction and empirically assay the validity of the ICM principle for text data using minimum description length. We conduct an extensive meta-analysis of over 100 published SSL and 30 DA studies, and find that the results are consistent with our expectations based on causal insights. This work presents the first attempt to analyze the ICM principle in NLP, and provides constructive suggestions for future modeling choices. Code available at https://github.com/zhijing-jin/icm4nlp

In this paper, we introduce complexity-aware planning for finite-horizon deterministic finite automata with rewards as outputs, based on Kolmogorov complexity. Kolmogorov complexity is considered since it can detect computational regularities of deterministic optimal policies. We present a planning objective yielding an explicit trade-off between a policy's performance and complexity. It is proven that maximising this objective is non-trivial in the sense that dynamic programming is infeasible. We present two algorithms obtaining low-complexity policies, where the first algorithm obtains a low-complexity optimal policy, and the second algorithm finds a policy maximising performance while maintaining local (stage-wise) complexity constraints. We evaluate the algorithms on a simple navigation task for a mobile robot, where our algorithms yield low-complexity policies that concur with intuition.

We are interested in understanding the underlying generation process for long sequences of symbolic events. To do so, we propose COSSU, an algorithm to mine small and meaningful sets of sequential rules. The rules are selected using an MDL-inspired criterion that favors compactness and relies on a novel rule-based encoding scheme for sequences. Our evaluation shows that COSSU can successfully retrieve relevant sets of closed sequential rules from a long sequence. Such rules constitute an interpretable model that exhibits competitive accuracy for the tasks of next-element prediction and classification.

We introduce a method to determine if a certain capability helps to achieve an accurate model of given data. We view labels as being generated from the inputs by a program composed of subroutines with different capabilities, and we posit that a subroutine is useful if and only if the minimal program that invokes it is shorter than the one that does not. Since minimum program length is uncomputable, we instead estimate the labels' minimum description length (MDL) as a proxy, giving us a theoretically-grounded method for analyzing dataset characteristics. We call the method Rissanen Data Analysis (RDA) after the father of MDL, and we showcase its applicability on a wide variety of settings in NLP, ranging from evaluating the utility of generating subquestions before answering a question, to analyzing the value of rationales and explanations, to investigating the importance of different parts of speech, and uncovering dataset gender bias.

Block modeling has been used extensively in many domains including social science, spatial temporal data analysis and even medical imaging. Original formulations of the problem modeled it as a mixed integer programming problem, but were not scalable. Subsequent work relaxed the discrete optimization requirement, and showed that adding constraints is not straightforward in existing approaches. In this work, we present a new approach based on constraint programming, allowing discrete optimization of block modeling in a manner that is not only scalable, but also allows the easy incorporation of constraints. We introduce a new constraint filtering algorithm that outperforms earlier approaches, in both constrained and unconstrained settings, for an exhaustive search and for a type of local search called Large Neighborhood Search. We show its use in the analysis of real datasets. Finally, we show an application of the CP framework for model selection using the Minimum Description Length principle.

We consider the question of sequential prediction under the log-loss in terms of cumulative regret. Namely, given a hypothesis class of distributions, learner sequentially predicts the (distribution of the) next letter in sequence and its performance is compared to the baseline of the best constant predictor from the hypothesis class. The well-specified case corresponds to an additional assumption that the data-generating distribution belongs to the hypothesis class as well. Here we present results in the more general misspecified case. Due to special properties of the log-loss, the same problem arises in the context of competitive-optimality in density estimation, and model selection. For the $d$-dimensional Gaussian location hypothesis class, we show that cumulative regrets in the well-specified and misspecified cases asymptotically coincide. In other words, we provide an $o(1)$ characterization of the distribution-free (or PAC) regret in this case -- the first such result as far as we know. We recall that the worst-case (or individual-sequence) regret in this case is larger by an additive constant ${d\over 2} + o(1)$. Surprisingly, neither the traditional Bayesian estimators, nor the Shtarkov's normalized maximum likelihood achieve the PAC regret and our estimator requires special "robustification" against heavy-tailed data. In addition, we show two general results for misspecified regret: the existence and uniqueness of the optimal estimator, and the bound sandwiching the misspecified regret between well-specified regrets with (asymptotically) close hypotheses classes.

Can we infer all the failed components of an infrastructure network, given a sample of reachable nodes from supply nodes? One of the most critical post-disruption processes after a natural disaster is to quickly determine the damage or failure states of critical infrastructure components. However, this is non-trivial, considering that often only a fraction of components may be accessible or observable after a disruptive event. Past work has looked into inferring failed components given point probes, i.e. with a direct sample of failed components. In contrast, we study the harder problem of inferring failed components given partial information of some `serviceable' reachable nodes and a small sample of point probes, being the first often more practical to obtain. We formulate this novel problem using the Minimum Description Length (MDL) principle, and then present a greedy algorithm that minimizes MDL cost effectively. We evaluate our algorithm on domain-expert simulations of real networks in the aftermath of an earthquake. Our algorithm successfully identify failed components, especially the critical ones affecting the overall system performance.

Pattern mining is well established in data mining research, especially for mining binary datasets. Surprisingly, there is much less work about numerical pattern mining and this research area remains under-explored. In this paper, we propose Mint, an efficient MDL-based algorithm for mining numerical datasets. The MDL principle is a robust and reliable framework widely used in pattern mining, and as well in subgroup discovery. In Mint we reuse MDL for discovering useful patterns and returning a set of non-redundant overlapping patterns with well-defined boundaries and covering meaningful groups of objects. Mint is not alone in the category of numerical pattern miners based on MDL. In the experiments presented in the paper we show that Mint outperforms competitors among which Slim and RealKrimp.

This paper addresses the issue of detecting hierarchical changes in latent variable models (HCDL) from data streams. There are three different levels of changes for latent variable models: 1) the first level is the change in data distribution for fixed latent variables, 2) the second one is that in the distribution over latent variables, and 3) the third one is that in the number of latent variables. It is important to detect these changes because we can analyze the causes of changes by identifying which level a change comes from (change interpretability). This paper proposes an information-theoretic framework for detecting changes of the three levels in a hierarchical way. The key idea to realize it is to employ the MDL (minimum description length) change statistics for measuring the degree of change, in combination with DNML (decomposed normalized maximum likelihood) code-length calculation. We give a theoretical basis for making reliable alarms for changes. Focusing on stochastic block models, we employ synthetic and benchmark datasets to empirically demonstrate the effectiveness of our framework in terms of change interpretability as well as change detection.