Bitcoin, and cryptocurrencies in general, are influenced by a variety of factors that can lead to their rise and fall in value. Understanding these factors is crucial for anyone interested in predicting Bitcoin's price using machine learning or other quantitative methods. Here are some of the key factors affecting Bitcoin's price:

1. Supply and Demand: This is a primary economic principle that drives the value of any commodity, including Bitcoin. A limited supply (due to the capped amount of 21 million Bitcoins) coupled with increasing demand can drive up the price. 2100

2. Regulation News: Any news regarding regulatory actions, either for or against Bitcoin and cryptocurrencies, can influence prices. Countries or states banning Bitcoin, for example, can lead to short-term declines.

3. Media Influence: Positive or negative media attention can lead to increased buying or selling activities.

4. Market Manipulation: "Whales", or large holders of Bitcoin, have the capacity to manipulate currency valuations. Accordingly, market movements could sometimes be arbitrary and not based on external news or events.

5. Technological Changes and Innovations: Updates, forks, or any other changes to the underlying technology can impact prices.

6. Macro Economic Factors: Economic events, such as recessions or financial crises, can influence investors to move into decentralized currencies like Bitcoin.

7. Speculation: As with any asset, speculation plays a significant role. Many people buy Bitcoin in the hopes that it will appreciate in value.

8. Integration: Bitcoin's adoption by merchants, payment platforms, and banking systems, as well as the integration into mainstream systems and its use as a means of transaction, can affect its value.

9. Other Markets: Movements in other markets, like the stock market, can indirectly influence the demand for Bitcoin, especially if investors are looking for alternative places to park their money.

10. Geopolitical Events: Events such as financial sanctions, wars, or major political changes can influence the demand for Bitcoin as it might be viewed as an alternative to traditional currencies.

Given these factors, building a predictive model for Bitcoin's price using machine learning is certainly possible but comes with challenges:

1. Noisy Data: The Bitcoin market is extremely volatile and can move based on rumors, which means the data can be noisy. This noise makes it challenging for machine learning models to identify long-term trends and patterns.

2. Non-Stationarity: Financial time series data, including Bitcoin prices, are typically non-stationary. This means that their statistical properties change over time, making them difficult to model.

3. Overfitting: Given the multitude of factors and the complex interplay between them, there's a risk of overfitting where the model might perform exceptionally well on training data but poorly on unseen data.

4. External Shocks: Sudden unforeseeable events can drastically change the trajectory of Bitcoin's price.

Despite these challenges, machine learning can still provide insights into price movements and potentially predict short-term changes. But it's important to approach this task with caution and skepticism, combining machine learning models with domain expertise and other traditional methods of financial analysis. Always remember that predicting financial markets is inherently risky, and no model can guarantee future performance.