arXiv subjects

Ole-Christoffer Granmo

Publications and source records attributed to Ole-Christoffer Granmo.

At least 73 records · Page 4Linked to original sources

arXiv2020

Extending the Tsetlin Machine With Integer-Weighted Clauses for Increased Interpretability

Despite significant effort, building models that are both interpretable and accurate is an unresolved challenge for many pattern recognition problems. In general, rule-based and linear models lack accuracy, while deep learning interpretability is based on rough approximations of the underlying inference. Using a linear combination of conjunctive clauses in propositional logic, Tsetlin Machines (TMs) have shown competitive performance on diverse benchmarks. However, to do so, many clauses are needed, which impacts interpretability. Here, we address the accuracy-interpretability challenge in machine learning by equipping the TM clauses with integer weights. The resulting Integer Weighted TM (IWTM) deals with the problem of learning which clauses are inaccurate and thus must team up to obtain high accuracy as a team (low weight clauses), and which clauses are sufficiently accurate to operate more independently (high weight clauses). Since each TM clause is formed adaptively by a team of Tsetlin Automata, identifying effective weights becomes a challenging online learning problem. We address this problem by extending each team of Tsetlin Automata with a stochastic searching on the line (SSL) automaton. In our novel scheme, the SSL automaton learns the weight of its clause in interaction with the corresponding Tsetlin Automata team, which, in turn, adapts the composition of the clause by the adjusting weight. We evaluate IWTM empirically using five datasets, including a study of interpetability. On average, IWTM uses 6.5 times fewer literals than the vanilla TM and 120 times fewer literals than a TM with real-valued weights. Furthermore, in terms of average F1-Score, IWTM outperforms simple Multi-Layered Artificial Neural Networks, Decision Trees, Support Vector Machines, K-Nearest Neighbor, Random Forest, XGBoost, Explainable Boosting Machines, and standard and real-value weighted TMs.

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arXiv2020

Increasing the Inference and Learning Speed of Tsetlin Machines with Clause Indexing

The Tsetlin Machine (TM) is a machine learning algorithm founded on the classical Tsetlin Automaton (TA) and game theory. It further leverages frequent pattern mining and resource allocation principles to extract common patterns in the data, rather than relying on minimizing output error, which is prone to overfitting. Unlike the intertwined nature of pattern representation in neural networks, a TM decomposes problems into self-contained patterns, represented as conjunctive clauses. The clause outputs, in turn, are combined into a classification decision through summation and thresholding, akin to a logistic regression function, however, with binary weights and a unit step output function. In this paper, we exploit this hierarchical structure by introducing a novel algorithm that avoids evaluating the clauses exhaustively. Instead we use a simple look-up table that indexes the clauses on the features that falsify them. In this manner, we can quickly evaluate a large number of clauses through falsification, simply by iterating through the features and using the look-up table to eliminate those clauses that are falsified. The look-up table is further structured so that it facilitates constant time updating, thus supporting use also during learning. We report up to 15 times faster classification and three times faster learning on MNIST and Fashion-MNIST image classification, and IMDb sentiment analysis.

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arXiv2020

A Regression Tsetlin Machine with Integer Weighted Clauses for Compact Pattern Representation

The Regression Tsetlin Machine (RTM) addresses the lack of interpretability impeding state-of-the-art nonlinear regression models. It does this by using conjunctive clauses in propositional logic to capture the underlying non-linear frequent patterns in the data. These, in turn, are combined into a continuous output through summation, akin to a linear regression function, however, with non-linear components and unity weights. Although the RTM has solved non-linear regression problems with competitive accuracy, the resolution of the output is proportional to the number of clauses employed. This means that computation cost increases with resolution. To reduce this problem, we here introduce integer weighted RTM clauses. Our integer weighted clause is a compact representation of multiple clauses that capture the same sub-pattern-N repeating clauses are turned into one, with an integer weight N. This reduces computation cost N times, and increases interpretability through a sparser representation. We further introduce a novel learning scheme that allows us to simultaneously learn both the clauses and their weights, taking advantage of so-called stochastic searching on the line. We evaluate the potential of the integer weighted RTM empirically using six artificial datasets. The results show that the integer weighted RTM is able to acquire on par or better accuracy using significantly less computational resources compared to regular RTMs. We further show that integer weights yield improved accuracy over real-valued ones.

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arXiv2020

The Weighted Tsetlin Machine: Compressed Representations with Weighted Clauses

The Tsetlin Machine (TM) is an interpretable mechanism for pattern recognition that constructs conjunctive clauses from data. The clauses capture frequent patterns with high discriminating power, providing increasing expression power with each additional clause. However, the resulting accuracy gain comes at the cost of linear growth in computation time and memory usage. In this paper, we present the Weighted Tsetlin Machine (WTM), which reduces computation time and memory usage by weighting the clauses. Real-valued weighting allows one clause to replace multiple, and supports fine-tuning the impact of each clause. Our novel scheme simultaneously learns both the composition of the clauses and their weights. Furthermore, we increase training efficiency by replacing $k$ Bernoulli trials of success probability $p$ with a uniform sample of average size $p k$, the size drawn from a binomial distribution. In our empirical evaluation, the WTM achieved the same accuracy as the TM on MNIST, IMDb, and Connect-4, requiring only $1/4$, $1/3$, and $1/50$ of the clauses, respectively. With the same number of clauses, the WTM outperformed the TM, obtaining peak test accuracies of respectively $98.63\%$, $90.37\%$, and $87.91\%$. Finally, our novel sampling scheme reduced sample generation time by a factor of $7$.

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arXiv2019

The Convolutional Tsetlin Machine

Convolutional neural networks (CNNs) have obtained astounding successes for important pattern recognition tasks, but they suffer from high computational complexity and the lack of interpretability. The recent Tsetlin Machine (TM) attempts to address this lack by using easy-to-interpret conjunctive clauses in propositional logic to solve complex pattern recognition problems. The TM provides competitive accuracy in several benchmarks, while keeping the important property of interpretability. It further facilitates hardware-near implementation since inputs, patterns, and outputs are expressed as bits, while recognition and learning rely on straightforward bit manipulation. In this paper, we exploit the TM paradigm by introducing the Convolutional Tsetlin Machine (CTM), as an interpretable alternative to CNNs. Whereas the TM categorizes an image by employing each clause once to the whole image, the CTM uses each clause as a convolution filter. That is, a clause is evaluated multiple times, once per image patch taking part in the convolution. To make the clauses location-aware, each patch is further augmented with its coordinates within the image. The output of a convolution clause is obtained simply by ORing the outcome of evaluating the clause on each patch. In the learning phase of the TM, clauses that evaluate to 1 are contrasted against the input. For the CTM, we instead contrast against one of the patches, randomly selected among the patches that made the clause evaluate to 1. Accordingly, the standard Type I and Type II feedback of the classic TM can be employed directly, without further modification. The CTM obtains a peak test accuracy of 99.4% on MNIST, 96.31% on Kuzushiji-MNIST, 91.5% on Fashion-MNIST, and 100.0% on the 2D Noisy XOR Problem, which is competitive with results reported for simple 4-layer CNNs, BinaryConnect, Logistic Circuits and an FPGA-accelerated Binary CNN.

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arXiv2019

A Tsetlin Machine with Multigranular Clauses

The recently introduced Tsetlin Machine (TM) has provided competitive pattern recognition accuracy in several benchmarks, however, requires a 3-dimensional hyperparameter search. In this paper, we introduce the Multigranular Tsetlin Machine (MTM). The MTM eliminates the specificity hyperparameter, used by the TM to control the granularity of the conjunctive clauses that it produces for recognizing patterns. Instead of using a fixed global specificity, we encode varying specificity as part of the clauses, rendering the clauses multigranular. This makes it easier to configure the TM because the dimensionality of the hyperparameter search space is reduced to only two dimensions. Indeed, it turns out that there is significantly less hyperparameter tuning involved in applying the MTM to new problems. Further, we demonstrate empirically that the MTM provides similar performance to what is achieved with a finely specificity-optimized TM, by comparing their performance on both synthetic and real-world datasets.

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arXiv2019

Towards Model-based Reinforcement Learning for Industry-near Environments

Deep reinforcement learning has over the past few years shown great potential in learning near-optimal control in complex simulated environments with little visible information. Rainbow (Q-Learning) and PPO (Policy Optimisation) have shown outstanding performance in a variety of tasks, including Atari 2600, MuJoCo, and Roboschool test suite. While these algorithms are fundamentally different, both suffer from high variance, low sample efficiency, and hyperparameter sensitivity that in practice, make these algorithms a no-go for critical operations in the industry. On the other hand, model-based reinforcement learning focuses on learning the transition dynamics between states in an environment. If these environment dynamics are adequately learned, a model-based approach is perhaps the most sample efficient method for learning agents to act in an environment optimally. The traits of model-based reinforcement are ideal for real-world environments where sampling is slow and for mission-critical operations. In the warehouse industry, there is an increasing motivation to minimise time and to maximise production. Currently, autonomous agents act suboptimally using handcrafted policies for significant portions of the state-space. In this paper, we present The Dreaming Variational Autoencoder v2 (DVAE-2), a model-based reinforcement learning algorithm that increases sample efficiency, hence enable algorithms with low sample efficiency function better in real-world environments. We introduce Deep Warehouse, a simulated environment for industry-near testing of autonomous agents in grid-based warehouses. Finally, we illustrate that DVAE-2 improves the sample efficiency for the Deep Warehouse compared to model-free methods.

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arXiv2019

A Neural Turing~Machine for Conditional Transition Graph Modeling

Graphs are an essential part of many machine learning problems such as analysis of parse trees, social networks, knowledge graphs, transportation systems, and molecular structures. Applying machine learning in these areas typically involves learning the graph structure and the relationship between the nodes of the graph. However, learning the graph structure is often complex, particularly when the graph is cyclic, and the transitions from one node to another are conditioned such as graphs used to represent a finite state machine. To solve this problem, we propose to extend the memory based Neural Turing Machine (NTM) with two novel additions. We allow for transitions between nodes to be influenced by information received from external environments, and we let the NTM learn the context of those transitions. We refer to this extension as the Conditional Neural Turing Machine (CNTM). We show that the CNTM can infer conditional transition graphs by empirically verifiying the model on two data sets: a large set of randomly generated graphs, and a graph modeling the information retrieval process during certain crisis situations. The results show that the CNTM is able to reproduce the paths inside the graph with accuracy ranging from 82,12% for 10 nodes graphs to 65,25% for 100 nodes graphs.

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arXiv2019

A Scheme for Continuous Input to the Tsetlin Machine with Applications to Forecasting Disease Outbreaks

In this paper, we apply a new promising tool for pattern classification, namely, the Tsetlin Machine (TM), to the field of disease forecasting. The TM is interpretable because it is based on manipulating expressions in propositional logic, leveraging a large team of Tsetlin Automata (TA). Apart from being interpretable, this approach is attractive due to its low computational cost and its capacity to handle noise. To attack the problem of forecasting, we introduce a preprocessing method that extends the TM so that it can handle continuous input. Briefly stated, we convert continuous input into a binary representation based on thresholding. The resulting extended TM is evaluated and analyzed using an artificial dataset. The TM is further applied to forecast dengue outbreaks of all the seventeen regions in the Philippines using the spatio-temporal properties of the data. Experimental results show that dengue outbreak forecasts made by the TM are more accurate than those obtained by a Support Vector Machine (SVM), Decision Trees (DTs), and several multi-layered Artificial Neural Networks (ANNs), both in terms of forecasting precision and F1-score.

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arXiv2019

The Regression Tsetlin Machine: A Tsetlin Machine for Continuous Output Problems

The recently introduced Tsetlin Machine (TM) has provided competitive pattern classification accuracy in several benchmarks, composing patterns with easy-to-interpret conjunctive clauses in propositional logic. In this paper, we go beyond pattern classification by introducing a new type of TMs, namely, the Regression Tsetlin Machine (RTM). In all brevity, we modify the inner inference mechanism of the TM so that input patterns are transformed into a single continuous output, rather than to distinct categories. We achieve this by: (1) using the conjunctive clauses of the TM to capture arbitrarily complex patterns; (2) mapping these patterns to a continuous output through a novel voting and normalization mechanism; and (3) employing a feedback scheme that updates the TM clauses to minimize the regression error. The feedback scheme uses a new activation probability function that stabilizes the updating of clauses, while the overall system converges towards an accurate input-output mapping. The performance of the RTM is evaluated using six different artificial datasets with and without noise, in comparison with the Classic Tsetlin Machine (CTM) and the Multiclass Tsetlin Machine (MTM). Our empirical results indicate that the RTM obtains the best training and testing results for both noisy and noise-free datasets, with a smaller number of clauses. This, in turn, translates to higher regression accuracy, using significantly less computational resources.

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arXiv2018

The Dreaming Variational Autoencoder for Reinforcement Learning Environments

Reinforcement learning has shown great potential in generalizing over raw sensory data using only a single neural network for value optimization. There are several challenges in the current state-of-the-art reinforcement learning algorithms that prevent them from converging towards the global optima. It is likely that the solution to these problems lies in short- and long-term planning, exploration and memory management for reinforcement learning algorithms. Games are often used to benchmark reinforcement learning algorithms as they provide a flexible, reproducible, and easy to control environment. Regardless, few games feature a state-space where results in exploration, memory, and planning are easily perceived. This paper presents The Dreaming Variational Autoencoder (DVAE), a neural network based generative modeling architecture for exploration in environments with sparse feedback. We further present Deep Maze, a novel and flexible maze engine that challenges DVAE in partial and fully-observable state-spaces, long-horizon tasks, and deterministic and stochastic problems. We show initial findings and encourage further work in reinforcement learning driven by generative exploration.

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arXiv2018

Using the Tsetlin Machine to Learn Human-Interpretable Rules for High-Accuracy Text Categorization with Medical Applications

Medical applications challenge today's text categorization techniques by demanding both high accuracy and ease-of-interpretation. Although deep learning has provided a leap ahead in accuracy, this leap comes at the sacrifice of interpretability. To address this accuracy-interpretability challenge, we here introduce, for the first time, a text categorization approach that leverages the recently introduced Tsetlin Machine. In all brevity, we represent the terms of a text as propositional variables. From these, we capture categories using simple propositional formulae, such as: if "rash" and "reaction" and "penicillin" then Allergy. The Tsetlin Machine learns these formulae from a labelled text, utilizing conjunctive clauses to represent the particular facets of each category. Indeed, even the absence of terms (negated features) can be used for categorization purposes. Our empirical comparison with Naïve Bayes, decision trees, linear support vector machines (SVMs), random forest, long short-term memory (LSTM) neural networks, and other techniques, is quite conclusive. The Tsetlin Machine either performs on par with or outperforms all of the evaluated methods on both the 20 Newsgroups and IMDb datasets, as well as on a non-public clinical dataset. On average, the Tsetlin Machine delivers the best recall and precision scores across the datasets. Finally, our GPU implementation of the Tsetlin Machine executes 5 to 15 times faster than the CPU implementation, depending on the dataset. We thus believe that our novel approach can have a significant impact on a wide range of text analysis applications, forming a promising starting point for deeper natural language understanding with the Tsetlin Machine.

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arXiv2018

Deep RTS: A Game Environment for Deep Reinforcement Learning in Real-Time Strategy Games

Reinforcement learning (RL) is an area of research that has blossomed tremendously in recent years and has shown remarkable potential for artificial intelligence based opponents in computer games. This success is primarily due to the vast capabilities of convolutional neural networks, that can extract useful features from noisy and complex data. Games are excellent tools to test and push the boundaries of novel RL algorithms because they give valuable insight into how well an algorithm can perform in isolated environments without the real-life consequences. Real-time strategy games (RTS) is a genre that has tremendous complexity and challenges the player in short and long-term planning. There is much research that focuses on applied RL in RTS games, and novel advances are therefore anticipated in the not too distant future. However, there are to date few environments for testing RTS AIs. Environments in the literature are often either overly simplistic, such as microRTS, or complex and without the possibility for accelerated learning on consumer hardware like StarCraft II. This paper introduces the Deep RTS game environment for testing cutting-edge artificial intelligence algorithms for RTS games. Deep RTS is a high-performance RTS game made specifically for artificial intelligence research. It supports accelerated learning, meaning that it can learn at a magnitude of 50 000 times faster compared to existing RTS games. Deep RTS has a flexible configuration, enabling research in several different RTS scenarios, including partially observable state-spaces and map complexity. We show that Deep RTS lives up to our promises by comparing its performance with microRTS, ELF, and StarCraft II on high-end consumer hardware. Using Deep RTS, we show that a Deep Q-Network agent beats random-play agents over 70% of the time. Deep RTS is publicly available at https://github.com/cair/DeepRTS.

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arXiv2018

FlashRL: A Reinforcement Learning Platform for Flash Games

Reinforcement Learning (RL) is a research area that has blossomed tremendously in recent years and has shown remarkable potential in among others successfully playing computer games. However, there only exists a few game platforms that provide diversity in tasks and state-space needed to advance RL algorithms. The existing platforms offer RL access to Atari- and a few web-based games, but no platform fully expose access to Flash games. This is unfortunate because applying RL to Flash games have potential to push the research of RL algorithms. This paper introduces the Flash Reinforcement Learning platform (FlashRL) which attempts to fill this gap by providing an environment for thousands of Flash games on a novel platform for Flash automation. It opens up easy experimentation with RL algorithms for Flash games, which has previously been challenging. The platform shows excellent performance with as little as 5% CPU utilization on consumer hardware. It shows promising results for novel reinforcement learning algorithms.

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arXiv2017

Towards a Deep Reinforcement Learning Approach for Tower Line Wars

There have been numerous breakthroughs with reinforcement learning in the recent years, perhaps most notably on Deep Reinforcement Learning successfully playing and winning relatively advanced computer games. There is undoubtedly an anticipation that Deep Reinforcement Learning will play a major role when the first AI masters the complicated game plays needed to beat a professional Real-Time Strategy game player. For this to be possible, there needs to be a game environment that targets and fosters AI research, and specifically Deep Reinforcement Learning. Some game environments already exist, however, these are either overly simplistic such as Atari 2600 or complex such as Starcraft II from Blizzard Entertainment. We propose a game environment in between Atari 2600 and Starcraft II, particularly targeting Deep Reinforcement Learning algorithm research. The environment is a variant of Tower Line Wars from Warcraft III, Blizzard Entertainment. Further, as a proof of concept that the environment can harbor Deep Reinforcement algorithms, we propose and apply a Deep Q-Reinforcement architecture. The architecture simplifies the state space so that it is applicable to Q-learning, and in turn improves performance compared to current state-of-the-art methods. Our experiments show that the proposed architecture can learn to play the environment well, and score 33% better than standard Deep Q-learning which in turn proves the usefulness of the game environment.

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arXiv2017

Thompson Sampling Guided Stochastic Searching on the Line for Deceptive Environments with Applications to Root-Finding Problems

The multi-armed bandit problem forms the foundation for solving a wide range of on-line stochastic optimization problems through a simple, yet effective mechanism. One simply casts the problem as a gambler that repeatedly pulls one out of N slot machine arms, eliciting random rewards. Learning of reward probabilities is then combined with reward maximization, by carefully balancing reward exploration against reward exploitation. In this paper, we address a particularly intriguing variant of the multi-armed bandit problem, referred to as the {\it Stochastic Point Location (SPL) Problem}. The gambler is here only told whether the optimal arm (point) lies to the "left" or to the "right" of the arm pulled, with the feedback being erroneous with probability $1-π$. This formulation thus captures optimization in continuous action spaces with both {\it informative} and {\it deceptive} feedback. To tackle this class of problems, we formulate a compact and scalable Bayesian representation of the solution space that simultaneously captures both the location of the optimal arm as well as the probability of receiving correct feedback. We further introduce the accompanying Thompson Sampling guided Stochastic Point Location (TS-SPL) scheme for balancing exploration against exploitation. By learning $π$, TS-SPL also supports {\it deceptive} environments that are lying about the direction of the optimal arm. This, in turn, allows us to solve the fundamental Stochastic Root Finding (SRF) Problem. Empirical results demonstrate that our scheme deals with both deceptive and informative environments, significantly outperforming competing algorithms both for SRF and SPL.

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arXiv2017

An Optimal Bayesian Network Based Solution Scheme for the Constrained Stochastic On-line Equi-Partitioning Problem

A number of intriguing decision scenarios revolve around partitioning a collection of objects to optimize some application specific objective function. This problem is generally referred to as the Object Partitioning Problem (OPP) and is known to be NP-hard. We here consider a particularly challenging version of OPP, namely, the Stochastic On-line Equi-Partitioning Problem (SO-EPP). In SO-EPP, the target partitioning is unknown and has to be inferred purely from observing an on-line sequence of object pairs. The paired objects belong to the same partition with probability $p$ and to different partitions with probability $1-p$, with $p$ also being unknown. As an additional complication, the partitions are required to be of equal cardinality. Previously, only sub-optimal solution strategies have been proposed for SO- EPP. In this paper, we propose the first optimal solution strategy. In brief, the scheme that we propose, BN-EPP, is founded on a Bayesian network representation of SO-EPP problems. Based on probabilistic reasoning, we are not only able to infer the underlying object partitioning with optimal accuracy. We are also able to simultaneously infer $p$, allowing us to accelerate learning as object pairs arrive. Furthermore, our scheme is the first to support arbitrary constraints on the partitioning (Constrained SO-EPP). Being optimal, BN-EPP provides superior performance compared to existing solution schemes. We additionally introduce Walk-BN-EPP, a novel WalkSAT inspired algorithm for solving large scale BN-EPP problems. Finally, we provide a BN-EPP based solution to the problem of order picking, a representative real-life application of BN-EPP.

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arXiv2017

Bayesian Unification of Gradient and Bandit-based Learning for Accelerated Global Optimisation

Bandit based optimisation has a remarkable advantage over gradient based approaches due to their global perspective, which eliminates the danger of getting stuck at local optima. However, for continuous optimisation problems or problems with a large number of actions, bandit based approaches can be hindered by slow learning. Gradient based approaches, on the other hand, navigate quickly in high-dimensional continuous spaces through local optimisation, following the gradient in fine grained steps. Yet, apart from being susceptible to local optima, these schemes are less suited for online learning due to their reliance on extensive trial-and-error before the optimum can be identified. In this paper, we propose a Bayesian approach that unifies the above two paradigms in one single framework, with the aim of combining their advantages. At the heart of our approach we find a stochastic linear approximation of the function to be optimised, where both the gradient and values of the function are explicitly captured. This allows us to learn from both noisy function and gradient observations, and predict these properties across the action space to support optimisation. We further propose an accompanying bandit driven exploration scheme that uses Bayesian credible bounds to trade off exploration against exploitation. Our empirical results demonstrate that by unifying bandit and gradient based learning, one obtains consistently improved performance across a wide spectrum of problem environments. Furthermore, even when gradient feedback is unavailable, the flexibility of our model, including gradient prediction, still allows us outperform competing approaches, although with a smaller margin. Due to the pervasiveness of bandit based optimisation, our scheme opens up for improved performance both in meta-optimisation and in applications where gradient related information is readily available.

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