MTH522

Information Gain stands as a pivotal concept in machine learning, especially in the realm of decision tree algorithms. It serves to quantify how effectively a feature can partition data into target classes, providing a means to prioritize features at each decision point. Essentially, Information Gain measures the difference in entropy before and after splitting a set on a specific attribute.

On the other hand, in the context of forecasting, there’s the method of simple exponential smoothing (SES). Ideal for data lacking strong trends or seasonality, SES assumes that future values will predominantly reflect the most recent observations, giving less weight to older data. This approach is characterized by historical weighting, simplicity in its input requirements, adaptability based on past errors, and a focus on recent data. By emphasizing the most recent information, SES streamlines pattern identification and minimizes the impact of noise and outliers in older data, making it particularly adept at forecasting in dynamic environments where variables exhibit volatility.

Today’s progress involved several steps in working with the code. Initially, I successfully conducted a count of parameters from the custom dataset, revealing that offense code 3115 was the most common. Subsequently, I endeavored to extract the data associated with offense code 3115 into a new dataset for exclusive analysis using latitude and longitude. Although the creation of the new dataset was successful, I encountered a mismatch issue when plotting the data on the map of Boston, specifically with latitude and longitude parameters. I am actively working to resolve this discrepancy.

In addition to spatial analysis, I aimed to plot offense codes along with their frequencies using matplotlib. Unfortunately, an error message pertaining to an invalid built-in function has surfaced. This is perplexing, considering the success of a similar method on another dataset. I am currently investigating the source of this error and will rectify it to proceed with plotting the graph. Furthermore, I plan to generate a Pareto Curve by the weekend, offering a comprehensive analysis of the dataset.

Today, my focus remained on the crime incident report dataset, where I worked on developing a code to extract data for specific crime codes over the span of eight years. The goal is to create a graph plotting latitude and longitude parameters, providing a visual representation of crime distribution in Boston. Additionally, I explored the Pareto curve method as a valuable tool for analyzing the dataset. This method involves plotting individual values in descending order, combining both bar and line charts. The line chart represents the cumulative total of the dataset, offering insights into the percentage contribution of each crime to the overall incident reports. I believe this Pareto curve will provide a nuanced understanding of how police allocate resources and which offenses dominate their workload. In the forthcoming days, my aim is to present the data through well-crafted graphs and visual representations.

Today, I continued to work over analyzing the data from the crime incident report. With initial analysis of the data in the last time, where the maximum number of incidents were reported for investigating a particular person, I started working towards analyzing the insights related to that parameter. I am currently working on a code, through which I will aim to combine the data of that particular crime or offense code with the parameters of longitude and latitude. Combining both the data parameters, we can try to work on the neighborhood which has the most reports for these types of incidents and hence, with that we should be able to say the particular crime prone neighborhood. In the coming days, I will continue to work over the code and also discuss this further with my team

Today in class, we delved into the neighborhood demographics dataset, exploring potential parameters for constructing a time series model. A noteworthy idea emerged: training the model on the last seven decades of data and using it to predict trends for the next one or two decades. Additionally, we delved into another dataset focused on crime incident reports, covering incidents reported in various areas of Boston from 2015 to the present. Notably, the dataset displayed a wide range of values for individual parameters. In our discussion, a proposed approach involved leveraging spatiotemporal analysis to gain insights into the data. The use of spatiotemporal analysis allows for a broader perspective, enabling us to comprehend datasets across larger spatial and temporal ranges. In the upcoming days, I plan to delve into understanding spatiotemporal analysis and integrating it with the crime incident reports dataset for a more comprehensive analysis.

The Z-test, a captivating statistical tool, operates as a numerical detective, aiding in the exploration of significant differences between sample data and our assumptions about the entire population. Picture dealing with a substantial set of data points: the Z-test becomes relevant when assessing whether the average of your sample significantly deviates from the expected population average, given some prior knowledge about the population, such as its standard deviation.

This tool proves particularly useful when handling large datasets, relying on the concept of a standard normal distribution resembling a bell curve often seen in statistics. By computing the Z-score and comparing it to values in a standard normal distribution table or using statistical software, one can determine whether the sample’s average differs significantly from the predicted value.

The Z-test finds application in various fields, from quality control to marketing research, serving as a truth-checker for data. However, a critical caveat exists: for optimal functioning, certain conditions must be met, such as the data being approximately normally distributed and possessing a known population variance. These assumptions act as the foundational pillars of statistical analysis, and if they are not solid, the reliability of the results may be compromised.

Time Series Forecasting emerges as a crucial analytical technique, transcending traditional statistical analysis to unveil hidden patterns and trends within sequential data. This dynamic field empowers decision-makers by leveraging historical data, deciphering temporal dependencies, and projecting future scenarios. In the realm of data science, Time Series Analysis serves as a linchpin, providing insight into the evolution of phenomena over time. It enables the dissection of historical data, revelation of seasonality, capture of cyclic behavior, and identification of underlying trends. Armed with this comprehension, one can navigate the realm of predictions, offering invaluable insights that inform decision-making across diverse domains. Time Series Forecasting, far from being just a statistical tool, serves as a strategic compass, enabling anticipation of market fluctuations, optimization of resource allocation, and enhancement of operational efficiency. Its applications span wide, from predicting stock prices and energy consumption to anticipating disease outbreaks and weather conditions, showcasing its vast and profound impact.

Imputing missing values using a decision tree involves predicting the absent values in a specific column based on other features in the dataset. Decision trees, a type of machine learning model, make decisions by following “if-then-else” rules based on input features, proving particularly adept at handling categorical data and intricate feature relationships. To apply this to a dataset, consider using a decision tree to impute missing values in the ‘armed’ column. Begin by ensuring other predictor columns are devoid of missing values and encoding categorical variables if necessary. Split the data into sets with known and missing ‘armed’ values, then train the decision tree using the former. Subsequently, use the trained model to predict and impute missing ‘armed’ values in the latter set. Optionally, evaluate the model’s performance using a validation set or cross-validation to gauge the accuracy of the imputation process.

Today’s class was quite engaging, featuring discussions about classmates’ projects and ideas. Later, we delved into a class focused on Decision Trees.

The Decision Tree algorithm functions by categorizing data, such as a set of animal traits, to identify a specific animal based on those characteristics. It begins by posing a question, like “Can the animal fly?” This question divides the animals into groups based on their responses, guiding the progression down the tree.

With each subsequent question, the tree further refines the groups, narrowing down the possibilities until it arrives at a conclusion regarding the identity of the animal in question. Trained using known data, the decision tree learns optimal inquiries (or data divisions) to efficiently arrive at accurate conclusions. Consequently, when presented with unfamiliar data, it applies its learned patterns to predict the identity of the animal.